First slide

Evaluation of definite integrals

Question

$\int_{- 1}^{1} (a x^{3} + b x) d x = 0, \forall a, b \in R$

Easy

A

any values of a and b
B

a > 0, b > 0 only
C

a > 0, b < 0 only
D

a < 0, b < 0 only

Solution

$\int_{- 1}^{1} a x^{3} + b x = 0 \forall a, b \in R$
$a x^{3} + b x$ is odd functions.

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