Evaluate - sin 4 x-dx

∫ _ #160; ^ #160; sin #160; #160;^ 4 xdx #160; Use the reduction formula ∫ _ #160; ^ #160; sin #160; #160;^ n ( x ) #16 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Basic Trigonometric Identities

Evaluate ∫ s...

Question

Evaluate
$\int {s i n}^{4} x . d x$

Open in App

Solution

$\int {sin}^{4} x d x$

$U s e t h e r e d u c t i o n f o r m u l a$

$\int {sin}^{n} (x) d x = \frac{n - 1}{n} \int {sin}^{n - 2} (x) \frac{cos (x) {sin}^{n - 1} (x)}{n}, w h e n n = 4$

$= - \frac{cos (x) {sin}^{3} (x)}{4} + \frac{3}{4} \int {sin}^{2} (x) d x$

$= - \frac{cos (x) {sin}^{3} (x)}{4} - \frac{3 cos (x) sin (x)}{8} + \frac{3 x}{8} + C$

Suggest Corrections

Similar questions

Evaluate : $\int \frac{x^{3}}{(x - 1) (x^{2} + 1)} d x .$

Evaluate $\int \frac{s i n x - x c o s x}{x (x + s i n x)}$ dx.

Q. Evaluate :

Evaluate : $\int_{0}^{π} \frac{x t a n x}{s e c x + t a n x} d x .$ OR Evaluate : $\int_{1}^{4} {|x-1|+|x-2|+|x-4|}dx.$

Evaluate: $\int_{0}^{\frac{π}{2}} \frac{s i n^{2} x}{s i n x + c o s x} d x .$

Evaluate: $\int_{- 1}^{2} (e^{3 x} + 7 x - 5) d x$ as a limit of sums.

$Evaluate : (i) (\frac{2}{- 3} \times \frac{5}{4}) + (\frac{5}{9} \times \frac{3}{- 10}) (i i) (2 \times \frac{1}{4}) - (\frac{- 18}{7} \times \frac{- 7}{15}) (i i i) (- 5 \times \frac{2}{15}) - (- 6 \times \frac{2}{9}) (i v) (\frac{8}{5} \times \frac{- 3}{2}) + (\frac{- 3}{10} \times \frac{9}{16})$

Join BYJU'S Learning Program

Evaluate∫sin4x.dx

∫sin4xdxUsethereductionformula∫sinn(x)dx=n−1n∫sinn−2(x)cos(x)sinn−1(x)n,whenn=4=−cos(x)sin3(x)4+34∫sin2(x)dx=−cos(x)sin3(x)4−3cos(x)sin(x)8+3x8+C

Evaluate
$\int {s i n}^{4} x . d x$