Question

Answer the following based on the following statements:

Assertion : ${\int }_0^{\pi /2}\frac{\sin x}{\sin x+\cos x}dx=\frac{\pi }{4}$

Reason: ${\int }_0^{a}f\left(x\right)dx={\int }_0^{a}f(a-x)dx$

• A. Both Assertion and Reason are correct and R is the correct explanation of Assertion
• B. Both Assertion and Reason are correct and R is not the correct explanation of Assertion
• C. Assertion is true and Reason is false
• D. Assertion is false and Reason is true

Answer 1

The correct option is A Both Assertion and Reason are correct and R is the correct explanation of Assertion

$f(\pi /2-x)$
$I={\int }_0^{\pi /2}\frac{sinx}{sinx+cosx}dx;I={\int }_0^{\pi /2}\frac{cosx}{sinx+cosx}$
$2I={\int }_0^{\pi /2}1dx=\pi /2$
$I=\pi /2$
$A\to true$
${\int }_0^{a}dx={\int }_0^{a}f(a-x)dx$
$R\to true$
R explains A.