The value of - 3 x 2 xdx is……….

We have, f(x) = - 3 x 2 xdx f( - x) = - 3 ( - 2) - 2 ( - x)dx = - f(x) Since, f(x) is an odd function. therefore, - 3 x 2 xdx = 0

Integrals — Class 12 Maths Solution

exemplar fill FillBlank NCERT Exemp. Q. 63,Page 169

Question

The value of $\int_{ - \pi }^\pi {{{\sin }^3}} x{\cos ^2}xdx$ is……….

Step-by-step Solution

We have, $f(x) = \int_{ - \pi }^\pi {{{\sin }^3}} x{\cos ^2}xdx$

$f( - x) = \int_{ - \pi }^\pi {{{\sin }^3}} ( - 2) - {\cos ^2}( - x)dx$

$= - f(x)$

Since, $f(x)$ is an odd function.
therefore,$\int_{ - \pi }^\pi {{{\sin }^3}} x{\cos ^2}xdx = 0$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.