Question

If f is continuous function then which of the following is INCORRECT:

• A. $\underset{-2}{\overset{2}{\int }}f\left(x\right)dx=\underset{0}{\overset{2}{\int }}\left(f\left(x\right)-f\left(-x\right)\right)dx$
• B. $\underset{-3}{\overset{5}{\int }}2f\left(x\right)dx=\underset{-6}{\overset{10}{\int }}f\left(x-1\right)dx$
• C. $\underset{-3}{\overset{5}{\int }}f\left(x\right)dx=\underset{-6}{\overset{10}{\int }}f\left(\frac{x}{2}\right)dx$
• D. $\underset{-3}{\overset{5}{\int }}f\left(x\right)dx=\underset{-2}{\overset{6}{\int }}f\left(x-1\right)dx$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $\underset{-2}{\overset{2}{\int }}f\left(x\right)dx=\underset{0}{\overset{2}{\int }}\left(f\left(x\right)-f\left(-x\right)\right)dx$
B $\underset{-3}{\overset{5}{\int }}2f\left(x\right)dx=\underset{-6}{\overset{10}{\int }}f\left(x-1\right)dx$
C $\underset{-3}{\overset{5}{\int }}f\left(x\right)dx=\underset{-6}{\overset{10}{\int }}f\left(\frac{x}{2}\right)dx$
D $\underset{-3}{\overset{5}{\int }}f\left(x\right)dx=\underset{-2}{\overset{6}{\int }}f\left(x-1\right)dx$