This is a hard problem to price in this format. It took me a page on paper. Right here are the vital points:

1) Pull out the 20π. The is simply a constant.

You are watching: Integral of sin^3x cos^2x

2) usage a trig substitution: sin(3x) = 3sin(x) - 4 sin3(x) and also cos(2x) = 1 - 2sin2(x)

3) Multiply the end the resulting 2 binomials to acquire 20π∫8sin5(x) -10sin3(x) + 3sin(x) dx

4) rest this into 3 separate integrals. Because that the first 160π∫sin5(x), rest it into 160π∫sin4(x)sin(x) and then substitute in the trig identification <1-cos2(x)>2 because that sin4(x) then usage a u substitution u = cos(x). The an outcome after you space all completed is 160π<-cos(x) +2/3cos3(x) - 1/5cos5(x)>

5) for the second integral -200π∫sin3(x)dx, repeat the procedure above and also you eventually get: -200π<-cos(x) +1/3cos3(x)

6) The third integral conveniently solves to -60πcos(x)

7) placed them all together and also combine like terms and you get: -20πcos(x) +40πcos3(x) - 160/5πcos5(x) + C

upvote • 0 Downvote
More
Report

Tutor
5 (3)

Calculus

view tutors like this
view tutors prefer this

Note sin x cos y = 1/2

sin(3x) cos(2x) = 1/2

∫π20sin(3x)cos(2x)dx = 20 π ∫(1/2)dx = 10π ∫dx = 10 π <(-1/5) cos(5x) + (-1)cos(x)> + C=-2 π + C ﻿where C is any kind of constant

rise • 0 Downvote
Comment • 1
More
Report

QZ P.

you re welcome remember to add the + C because that the indefinite integral
Report

## Still looking for help? acquire the ideal answer, fast.

ask a inquiry for totally free

gain a free answer to a quick problem. Many questions answered within 4 hours.

OR
uncover an digital Tutor now

pick an expert and meet online. No packages or subscriptions, pay just for the time you need.

¢ € £ ¥ ‰ µ · • § ¶ ß ‹ › « » > ≤ ≥ – — ¯ ‾ ¤ ¦ ¨ ¡ ¿ ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃ ∅ ∇ ∗ ∝ ∠ ´ ¸ ª º † ‡ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù Ú Û Ü Ý Ÿ Þ à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ø œ š ù ú û ü ý þ ÿ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℵ ϖ ℜ ϒ ℘ ℑ ← ↑ → ↓ ↔ ↵ ⇐ ⇑ ⇒ ⇓ ⇔ ∴ ⊂ ⊃ ⊄ ⊆ ⊇ ⊕ ⊗ ⊥ ⋅ ⌈ ⌉ ⌊ ⌋ 〈 〉 ◊

### RELATED TOPICS

math Algebra 2 Geometry Precalculus Algebra Pre Calculus limits Functions Math help Trig ... Derivative Ap Calc Ap Calculus Calc Derivatives Trigonometric Identities Trigonometric functions Calculus 3 Calculus 2 Calculus 1

### RELATED QUESTIONS

deserve to I send A math EQUATION I'M HAVING troubles WITH?

If i have rational function and it has actually a molecule that can be factored and the denominator is already factored out would certainly I leveling by factoring the numerator?

exactly how do i uncover where a function is discontinuous if the bottom part of the role has been factored out?

discover the limit together it philosophies -3 in the equation (6x+9)/x^4+6x^3+9x^2

Grant J.

4.6 (22)

Sandra L.

4.9 (491)

Rachael L.

5.0 (706)
See more tutors

### uncover an digital tutor

A attach to the app was sent to her phone.

See more: Pokin Drive Belt For Cub Cadet Ltx 1050 Drive Belt Replacement

Please carry out a valid phone number.
obtain to understand us
find out with united state
work with united state
Let’s store in touch
Need an ext help?

Learn much more about just how it works

Tutors by subject
Tutors by location
Sitemap regards to Use Privacy plan
© 2005 - 2022 rwandachamber.org, Inc, a department of IXL learning - all Rights booked |