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$\begin{array}{l}LetI={\displaystyle {\int }_{-\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}si{n}^2}xdx.\\ I=2{\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}si{n}^2}xd(x)-----(i)\\ =2{\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}si{n}^2}\left(\frac{\pi }{2}-x\right)dx\\ =2{\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}co{s}^2}xdx-----(ii)\end{array}$

$\begin{array}{l}\left(i\right)+\left(ii\right)weget,\\ ?{\displaystyle {\int }_{-a}^{a}f}(x)dx=2{\displaystyle {\int }_0^{a}f}(x)dxiff(-x)=f(x)\end{array}$

$\begin{array}{l}f\left(x\right) = si{n}^{2}x\hfill \end{array}$

$\begin{array}{ll} f\left(x\right) = si{n}^2\left(–x\right) = {\left(–1\right)}^{2}si{n}^{2}x= si{n}^{2}x\hfill & \hfill \end{array}$

$\begin{array}{l}if,f\left(x\right) =f\left(–x\right)\hfill \end{array}$

$\begin{array}{l}\left\{?{\displaystyle {\int }_0^{a}f}(x)dx={\displaystyle {\int }_0^{a}f}(a-x)dx\right\}\\ 2I=2{\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left(si{n}^{2}x+co{s}^{2}x\right)}dx\\ I={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}1}dx=\frac{\pi }{2}.\end{array}$

Acc to Shiksha Rankings, some top MS universities in Finland are mentioned below for Indian students-

• Aalto University- #1 in MS in Finland
• University of Helsinki- #2 in MS in Finland
• Tampere University- #3 in MS in Finland
• University of Turku- #4 in MS in Finland
• University of Oulu- #5 in MS in Finland
• Lappeenranta University of Technology- #6 in MS in Finland
• University of Eastern Finland- #7 in MS in Finland

Shri Guru Ram Rai University DPharma applications can be filled out online. The forms are made available on the university's official website. The following are the steps to apply:

1. Go to the official website of the university.

2. Scroll down and click on the 'Apply Now' banner.

3. Register with basic details to make a new candidature account.

4. Log in and fill out the application form. 

5. Pay the application fee and click on the submit button.

$\begin{array}{l}LetI={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}(}2logsinx-logsin2x)dx\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left(logsi{n}^{2}x-logsin2x\right)}dx\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}log}\frac{si{n}^{2}x}{sin2x}dx\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}log}\frac{si{n}^{2}x}{2sinx·cosx}dx.\end{array}$

$\begin{array}{l}I={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}log}\left(\frac{1}{2}tanx\right)dx-----(i)\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left[log\frac{1}{2}tan\left(\frac{\pi }{2}-x\right)\right]}dx{\displaystyle {\int }_0^{a}f(x)dx=}{\displaystyle {\int }_0^{a}f(a-x)dx}\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left(log\frac{1}{2}cotx\right)}dx-----(ii)\\ \left(i\right)+\left(ii\right)\\ I+I={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left[log\left(\frac{1}{2}tanx\right)+log\left(\frac{1}{2}cotx\right)\right]}dx\\ 2I={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}log}\left(\frac{1}{2}tanx\times \frac{1}{2}cotx\right)dx\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}log}\frac{1}{4}dx.\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}(}log1-log4)dx\\ =0–log4{\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}d}x\\ =–log4\times \frac{\pi }{2}\\ I=-\frac{log{2}^2\times \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{2}\\ =-\frac{2log2\times \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{2}\\ =\frac{-\pi }{2}log2.\end{array}$

Yes, candidates seeking admission to the BTech in Food Technology programme at BHU must have studied Mathematics in Class 12. As per the eligibility criteria specified by the university for admission to the programme, candidates must have passed Class 12 with Physics, Chemistry & Mathematics (PCM), or Physics, Chemistry, Mathematics & Biology (PCMB), with English. Further, they must have scored a minimum aggregate of 50% in Class 12.

Post graduation from top MS university in Finland, graduates get good job opportunities in global companies. Below mentioned are the estimated placement salaries offered to students at the top universities for an MS in Finland:

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PW Institute of Innovation also offers direct admissions based on Class 12 and national-level entrance exam scores. Students can check the table below for more details:

The college offers UG programmes, namely, BTech, BBA and BVoc. Candidates must pass Class 12 for the UG course admission. The application process at the PW Institute of Innovation, Pune is conducted online. The selection criteria for all three courses are based on merit or entrance exam scores as per the course requirements.

$\begin{array}{l}LetI={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$4$}\right.}log}(1+tanx)dx-----(i)\\ ={\displaystyle {\int }_0^{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$4$}\right.}log}\left[1+tan\left(\frac{\pi }{4}-x\right)\right]dx?\{{\displaystyle {\int }_0^{a}f(x)dx=}{\displaystyle {\int }_0^{a}f(a-x)dx}\\ ={\displaystyle {\int }_0^{\frac{\pi }{4}}log}\left[1+\frac{tan\frac{\pi }{4}-tanx}{1+tan\frac{\pi }{4}tanx}\right]dx\\ ={\displaystyle {\int }_0^{\frac{\pi }{4}}log}·\left\{1+\frac{1-tanx}{1+tanx}\right\}dx\\ ={\displaystyle {\int }_0^{\frac{\pi }{4}}log}\left\{\frac{1+tanx+1-tanx}{1+tanx}\right\}dx\\ I={\displaystyle {\int }_0^{\frac{\pi }{4}}log}\left(\frac{2}{1+tanx}\right)dx-----(ii)\\ Adding\left(i\right)\&\left(ii\right)weget,\\ I+I={\displaystyle {\int }_0^{\frac{\pi }{4}}\left\{log(1+tanx)+log\left(\frac{2}{1+tanx}\right)\right\}}dx\\ I={\displaystyle {\int }_0^{\frac{\pi }{4}}log}\left\{\underset{\_}{1+tanx}\times \frac{2}{1+tanx}\right\}dx\\ ={\displaystyle {\int }_0^{\frac{\pi }{4}}log}2dx\\ ={[xlog2]}_0^{\frac{\pi }{4}}\\ =log2\left[\frac{\pi }{4}-0\right]=\frac{\pi }{4}log2\\ I=\frac{\pi }{8}log2.\end{array}$

Below are the details of minimum score requirements for admission to some popular universities in Finland:

Candidates wanting to take admission in PGDM course of I-Business Institute have to pay the required application fees. The institute's application fee amount is INR 1,100. Candidates shall pay the application fee amount via net banking or a debit/ credit card. It is advisable to keep the fee payment receipt safe for future references.

In an F1 visa interview, applicants can be questionsed about - test scores, English language proficiency levels, high school transcripts, common interests, reasons for studying in the chosen university, etc. These questions help interviewers if applicants will be able to do justics as a student in the institution opted to attend.

Yes, fulfilling the English language requirement is one of the major admission requirements for MS in Finland. Universities in Finland accepts major English exam scores as a proof of proficiency in the English language and students can refer to the table below for minimum score details:

The applicants attending the F1 visa interview for studying in USA, can expect the following areas for discussion:

• Study plans - Higher education, coursework
• Financial standing - who is sponsoring education, what kind of jobs parents do and how to support oneself for future financially
• Intent to return to home country - applicant's intention of staying back in USA if any, if there are any relatives long term plans after education
• Personal history - medical illness, backlogs (if any) and kind of relationship with parents/guardians back home