Statement I: ∫₋₂² (x²)/(1 + 2ˣ) dx = 8/3. Statement II: ∫_(-a)^a f(x) dx = 2 ∫₀^a f(x) dx, if f(x) is an even function.

Answer: (a) Both the statements are true. Correct: (a)

Mathematics20251 markMCQIntegrals

Choose the correct option.

Statement I: ∫₋₂² (x²)/(1 + 2ˣ) dx = 8/3. Statement II: ∫_(-a)^a f(x) dx = 2 ∫₀^a f(x) dx, if f(x)…

Statement I: $\int_{-2}^2 \frac{x^2}{1 + 2^x} \, dx = \frac{8}{3}$. Statement II: $\int_{-a}^a f(x) \, dx = 2 \int_0^a f(x) \, dx$, if $f(x)$ is an even function.

(a)Both the statements are true.
(b)Both the statements are false.
(c)Statement I is false, and statement II is true.
(d)Statement I is true, and statement II is false.

Answer

Official answer key

Correct option: (a)

Answer: (a) Both the statements are true.