The value of -2-2 2sin x d x-5-24sin -1log 2x-2 d x is equal to

The correct option is B 5π/4 ∫_ π/2^π/22^sinx dx+∫_5/2^4sin^ 1log_2(x 2) dx ∫_a^bf(x)dx+∫_f(a)^f(b)f^ 1(x)dx=bf(b) af(a) ∫_ π/2^π/2(2+2^sinx)dx+∫_5/2^4sin^ 1( ...

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Byju's Answer

Standard XII

Mathematics

Property 2

The value of ...

Question

The value of $\int_{- \frac{π}{2}}^{\frac{π}{2}} 2^{s i n x} d x + \int_{\frac{5}{2}}^{4} s i n^{- 1} l o g_{2} (x - 2) d x$ is equal to

$\frac{5 π}{4}$

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$π$

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$\frac{3 π}{4}$

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$\frac{π}{4}$

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Solution

The correct option is A
$\frac{5 π}{4}$

$\int_{- \frac{π}{2}}^{\frac{π}{2}} 2^{s i n x} d x + \int_{\frac{5}{2}}^{4} s i n^{- 1} l o g_{2} (x - 2) d x$
$\int_{a}^{b} f (x) d x + \int_{f (a)}^{f (b)} f^{- 1} (x) d x = b f (b) - a f (a) \int_{- \frac{π}{2}}^{\frac{π}{2}} (2 + 2^{s i n x}) d x + \int_{\frac{5}{2}}^{4} s i n^{- 1} (l o g_{2} (x - 2)) d x = 2 π + \frac{5 π}{4}$

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The value of ∫π2−π22sinx dx+∫452sin−1log2(x−2)dx is equal to

The correct option is A 5π4 ∫π2−π22sinx dx+∫452sin−1log2(x−2)dx ∫baf(x)dx+∫f(b)f(a)f−1(x)dx=bf(b)−af(a)∫π2−π2(2+2sinx)dx+∫452sin−1(log2(x−2))dx=2π+5π4

The value of $\int_{- \frac{π}{2}}^{\frac{π}{2}} 2^{s i n x} d x + \int_{\frac{5}{2}}^{4} s i n^{- 1} l o g_{2} (x - 2) d x$ is equal to