moyo34 moyo34
  • 02-08-2019
  • Engineering
contestada

integrate
∫cos²x sinx dx
​

Respuesta :

MathPhys
MathPhys MathPhys
  • 02-08-2019

Answer:

-⅓ cos³ x + C

Explanation:

∫ cos² x sin x dx

If u = cos x, then du = -sin dx.

∫ -u² du

Integrate using power rule:

-⅓ u³ + C

Substitute back:

-⅓ cos³ x + C

Answer Link
manissaha129
manissaha129 manissaha129
  • 28-08-2021

Answer:

Let, cos(x) = t => -sin(x)dx = dt => sin(x)dx = -dt

[tex] →\int { \cos}^{2}( x ).\ sin(x)dx \\ =- \int {t}^{2} dt = -\frac{ {t}^{3} }{3} + C = \boxed{ -\frac{1}{3} \cos^{3} (x) + C}✓[/tex]

  • -1/3cos³(x)+C is the right answer.
Answer Link

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