Question

15.-49-4x2

Answer 1

The integral of the function is given as,

∫ x 9−4 x 2 dx (1)

Consider, 9−4 x 2 =t.

Differentiate with respect to x.

, 9−4 x 2 =t −8xdx=dt

Substitute −8xdx=dt in equation (1) and then integrate.

∫ x 9−4 x 2 dx = −1 8 ∫ 1 t dt = −1 8 log| t |+C

Substitute 9−4 x 2 =t in above equation.

∫ x 9−4 x 2 dx = −1 8 log| t |+C = −1 8 log| 9−4 x 2 |+C