Question

integration of sin^7 x dx

Answer 1

Hii machiii ✋.


➡️ Integration for sin^7×dx

➡️ sin^7 (x) dx = ∫ sin ^6 (x) sin(x) dx. Let u = cos(x), du = -sin( x) dx = ∫ {1 - cos²(x)}³ sin(x) dx.

➡️ (1/7)cos7(x) - (3/5)cos5(x) + cos3(x) - cos(x) + C.

Answer 2

The integration of sin⁷ (x) dx is as follows:

(1/7)cos7(x) - (3/5)cos5(x) + cos3(x) - cos(x) + C

This can be found in the ways as follows :

• Let us consider, g = cos ( x )

• Differentiating both sides, we get,

        d g  =  - sin ( x ) d x

• Now, integrating sin⁷ (x) dx,

sin ⁷ ( x ) dx = ∫ sin⁶ ( x ) sin( x ) dx = ∫ { 1 - cos² ( x ) } ³ sin ( x ) dx  

                   =  (1/7)cos7(x) - (3/5)cos5(x) + cos3(x) - cos(x) + C