If -asin x d x-1-2- then a-2A- 0B- 1C- -D- -2 -3

The correct option is D 2π3If ∫_π2^asin x dx=. cos x |_π2^a 12= cos a+cosπ2 12= cos a ∵cosπ2=0 cos a= 12 Hence, a= 2π3 Here, the answer 12 is given, and ...

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Standard XII

Physics

Definite Integrals

If ∫πasin x d...

Question

If $a \int \frac{π}{2} sin x d x = \frac{1}{2}$ , then $a = ?$

0

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π

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- \frac{2 π}{3}

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Solution

The correct option is D $- \frac{2 π}{3}$
If $a \int \frac{π}{2} sin x d x = {\begin{matrix} - cos x \end{matrix} |}_{\frac{π}{2}}^{a}$
$\frac{1}{2} = - cos a + cos \frac{π}{2}$
$\frac{1}{2} = - cos a$
$∵ cos \frac{π}{2} = 0$
$cos a = - \frac{1}{2}$
Hence,
$a = - \frac{2 π}{3}$
Here, the answer $\frac{1}{2}$ is given, and we need to find the limit of integration.

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If a∫π2sinxdx=12, then a=?

The correct option is D −2π3If a∫π2sinxdx=−cosx|aπ2 12=−cosa+cosπ2 12=−cosa ∵cosπ2=0 cosa=−12 Hence, a=−2π3 Here, the answer 12 is given, and we need to find the limit of integration.

If $a \int \frac{π}{2} sin x d x = \frac{1}{2}$ , then $a = ?$