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Application of Integrals Ncert Solutions Maths class 12th Maths Class 12th Application of Integrals

13. Choose the correct answer:

Area of the region bounded by the curve y² = 4x,y - axis and the line y = 3 is:

(A) 2

(B) 9/4

(C) 9/3

(D) 9/2

26 Views | Posted 4 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

As $y = 3$ intersect $y^{2} = 4 x$ at Athen,

$\begin{array}{l} 3^{2} = 4 x \\ \Rightarrow x = \frac{9}{4} \end{array}$

$∴$ A has coordinate $(\frac{a}{4}, 3)$

Hence, area of curve = $\int_{y = 0}^{y = 3} x d y$

$\begin{array}{l} = \int_{0}^{3} \frac{y^{2}}{4} d y = {[\frac{y 3}{4 \times 3}]}_{0}^{3} \\ = \frac{3^{3}}{12} - \frac{0}{12} \\ = \frac{27}{12} = \frac{9}{4} u n i t^{2} \end{array}$

$∴$ Option (B) is correct

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Let a cure y = y(x) pass through the point (3, 3) and the area of the origin under this curve, above the x-axis and between the abscissae 3 and x (>3) be ${(\frac{y}{x})}^{3}$ . If the curve also passes through the point $(α, 6 \sqrt[]{10})$ in the first quadrant, then a is equal to………….

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$y^{2} = x, a = \frac{1}{4}$

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lim (x→∞) (∫? ^ (√x²+1) tan? ¹t dt) / x = lim (x→∞) (tan? ¹ (√x²+1) * (x/√ (x²+1) = lim (x→∞) (tan? ¹ x) * (x/√ (x²+1) = π/2

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A = ∫? ² lnx dx = 2ln2 – 1
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13. Choose the correct answer:

Area of the region bounded by the curve y² = 4x,y - axis and the line y = 3 is:

(A) 2

(B) 9/4

(C) 9/3

(D) 9/2