Let f be a one-one continuous function such that f 2-3 and f 5-7- Given -25 f x dx -17- then the value of the definite integral -37 f -1 x dx equalsA- 10B- 11C- 12D- 13

The correct option is C 12 y=f(x)⇒ x=f^ 1(y) and dy=f'(x)dx I=∫_3^7f^ 1(x)dx=∫_3^7f^ 1(y)dy =∫_2^5x.f'(x)dx Integrating by parts I=x.[f(x)]^5_2 ∫_2^5f(x)dx I ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Let f be a on...

Question

Let f be a one-one continuous function such that f(2) = 3 and f(5) = 7. Given $\int_{2}^{5} f (x) d x = 17$ , then the value of the definite integral $\int_{3}^{7} f^{- 1} (x) d x$ equals

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Solution

The correct option is C
12

$y = f (x) \Rightarrow x = f^{- 1} (y)$
and $d y = f^{'} (x) d x$
$I = \int_{3}^{7} f^{- 1} (x) d x = \int_{3}^{7} f^{- 1} (y) d y = \int_{2}^{5} x . f^{'} (x) d x$
Integrating by parts
$I = x . [f (x)]_{2}^{5} - \int_{2}^{5} f (x) d x I = 5 (7) - 2 (3) - 17 I = 12$

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Let f be a one-one continuous function such that f(2) = 3 and f(5) = 7. Given ∫52f(x)dx=17, then the value of the definite integral ∫73f−1(x)dx equals

The correct option is C 12 y=f(x)⇒x=f−1(y) and dy=f′(x)dx I=∫73f−1(x)dx=∫73f−1(y)dy=∫52x.f′(x)dx Integrating by parts I=x.[f(x)]52−∫52f(x)dxI=5(7)−2(3)–17I=12

Let f be a one-one continuous function such that f(2) = 3 and f(5) = 7. Given $\int_{2}^{5} f (x) d x = 17$ , then the value of the definite integral $\int_{3}^{7} f^{- 1} (x) d x$ equals

The correct option is C
12

$y = f (x) \Rightarrow x = f^{- 1} (y)$
and $d y = f^{'} (x) d x$
$I = \int_{3}^{7} f^{- 1} (x) d x = \int_{3}^{7} f^{- 1} (y) d y = \int_{2}^{5} x . f^{'} (x) d x$
Integrating by parts
$I = x . [f (x)]_{2}^{5} - \int_{2}^{5} f (x) d x I = 5 (7) - 2 (3) - 17 I = 12$