Evaluate the integral: sin² x cos³ x dx. 1²xcos³xdx= sin²xcos²xcosxdx 2xcos®xda = /sin? sin = [sin ²x (1+ sin²x) cosxdx= [(sin²x+ sinx) (cosxdx) Finish by letting u=cosx. [sin²xcos³xdx = [sin²xcos³xcosxdx = [sin ²x Finish by letting u = sinx. = = f (sin ²x + sin ²x (1+ sin²x) cosxdx = (sin ²x + sin+x) (cosxdx) "sinxcos®xd = / sin?xcos3xsinxde sin²x (1 – sin²x) sinxdx = [ (sin²x – sin*x) (sinxdx) - Finish by letting u = sinx. [sin ²xcos³xdx = [sin ²xcos²xcosxdx = [sin²x(1-sin³x) costes = f(sin²x – sin³x) (conxdx)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Evaluate the integral: sin² x cos³ x dx.
I sin
O
[si
sản-xcos®xdx = / sinxco:
= [sin ²x (1+ sin²x) cosxdx= [(sin²x+ sinx) (cosxdx)
Finish by letting u=cosx.
O
sin ²xcos²xcosxdx
/sin?xcosxdx = | si
= [₁ sin ²x (1 + sin²x) cosxdx = = f (sin²x +
Finish by letting u = sinx.
=
sin ²xcos²xcosxdx
"sinxcos®xd = / sin?xcos3xsinxde
si
x
sin ²x ( 1-sin²x) sinxdx=
Finish by letting u = sinx.
[si
= f(sin²x-s
+ sin+x) (cosxdx)
O
sin ²xcos²xcosxdx
/ sin3xcos®xdx = / sin3xc
= [sin ²x (1 - sin²x) cosxdx = [ (sin ²x – sinx) (cosxdx)
Finish by letting u = sinx.
sin ²xcos³xdx = sin²xcos²xcosxdx
- sin^x) (sinxdx)
= [sin ²x (1 - sin²x) cosxdx =
Finish by letting u=cosx.
-S (sin²x - - sin+x) (cosxdx)
Transcribed Image Text:Evaluate the integral: sin² x cos³ x dx. I sin O [si sản-xcos®xdx = / sinxco: = [sin ²x (1+ sin²x) cosxdx= [(sin²x+ sinx) (cosxdx) Finish by letting u=cosx. O sin ²xcos²xcosxdx /sin?xcosxdx = | si = [₁ sin ²x (1 + sin²x) cosxdx = = f (sin²x + Finish by letting u = sinx. = sin ²xcos²xcosxdx "sinxcos®xd = / sin?xcos3xsinxde si x sin ²x ( 1-sin²x) sinxdx= Finish by letting u = sinx. [si = f(sin²x-s + sin+x) (cosxdx) O sin ²xcos²xcosxdx / sin3xcos®xdx = / sin3xc = [sin ²x (1 - sin²x) cosxdx = [ (sin ²x – sinx) (cosxdx) Finish by letting u = sinx. sin ²xcos³xdx = sin²xcos²xcosxdx - sin^x) (sinxdx) = [sin ²x (1 - sin²x) cosxdx = Finish by letting u=cosx. -S (sin²x - - sin+x) (cosxdx)
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