Evaluate the following integrals : _ -9 ^9 x^3 4-x^2 d x

Question

Evaluate the following integrals : $\int_{-9}^9 \frac{x^3}{4-x^2} d x$

✓

Answer

Let $I=\int_{-9}^9 \frac{x^3}{4-x^2} d x$
Let $f(x)=\frac{x^3}{4-x^2}$
$
\therefore f(-x)=\frac{(-x)^3}{4-(-x)^2}=\frac{-x^3}{4+x^2}=-f(x)
$
$\therefore f$ is an odd function.
$\therefore \int_{-9}^9 f(x) d x=0$
i.e. $\int_{-9}^9 \frac{x^3}{4-x^2} d x=0$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Definite Integration (p-1)→Definite Integration (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.

→

Calculate the cost of living index.

Group	Base Year	Base Year	Current Year
	Price	Quantity	Price
Food	132	10	170
Clothing	154	12	160
Fuel & Lighting	164	20	180
House Rent	175	18	195
Miscellaneous	128	5	120