Question

STATEMENT-1 : The value of $\underset{\pi /3}{\overset{\pi /6}{\int }}\frac{1}{1+{\tan }^{3}x}dx$ is $\frac{\pi }{12}$
and
STATEMENT-2 : $\underset{a}{\overset{b}{\int }}f\left(x\right)dx=\underset{a}{\overset{b}{\int }}f(a+b+x)dx$

• A. Both statement I and statement II are correct and statement II is the correct explanation of statement I
• B. Both statement I and statement II are correct but statement II is not the correct explanation of statement I
• C. Statement II is correct but statement I is incorrect
• D. Statement I is correct but statement II is incorrect

Answer 1

The correct option is D Statement I is correct but statement II is incorrect

We know that
$\underset{a}{\overset{b}{\int }}f\left(x\right)dx=\underset{a}{\overset{b}{\int }}f(a+b-x)dx$
$\Rightarrow$ Statement-2 is false