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Draw a rough sketch of the given curve y = 1 + ? x + 1 ? , x = − 3 , x = 3 , y = 0  and find the area of the region bounded by them using integration.

0 4 Views | Posted 3 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a long answer type question as classified in NCERT Exemplar

    G i v e n     e q u a t i o n s     a r e     y = 1 + | x + 1 | ,     x = − 3     a n d     x = 3 ,     y = 0 T a k i n g     y = 1 + | x + 1 | ⇒                           y = 1 + x + 1 ⇒                           y = x + 2     a n d     y = 1 − x − 1         ⇒ y = − x O n     s o l v i n g     w e     g e t     x = − 1 ∴ A r e a     o f     r e q u i r e d     r e g i o n s           = ∫ − 3 − 1 − x   d x + ∫ − 1 3 ( x + 2 )   d x           = − [ x 2 2 ] − 3 − 1 + [ x 2 2 + 2 x ] − 1 3 = − [ 1 2 − 9 2 ] + [ ( 9 2 + 6 ) − ( 1 2 − 2 ) ]           = − ( − 4 ) + [ 2 1 2 + 3 2 ] = 4 + 1 2 = 1 6   s q .   u n i t s H e n c e ,     t h e     r e q u i r e d     a r e a = 1 6   s q .   u n i t s .

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