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C4 Integration help

Stuck on this one

By integration, find an exact value for the area

How would i integrate the second function, i dont seem to be getting anywhere with parts :s-smilie:

Can someone help me please

thanks

\int^\frac{\pi}{2}_\frac{\pi}{3} 9tsint dt - \int^\frac{\pi}{2}_\frac{\pi}{3}12sin^2tcostdt

Reply 1

Ludivico

devan5

\int^\frac{\pi}{2}_\frac{\pi}{3} 9tsint dt - \int^\frac{\pi}{2}_\frac{\pi}{3}12sin^2tcostdt

Susbtitution of u=sin(t) will work or just look at the derivative of

sin^3(t)

Reply 2

the greatest

for the last bit sin^2t is 1 - cos^2t so sub it in

for the first bit do integration by parts

Reply 3

JoshFlack

First integral by parts, second by inspection. Simples.

Reply 4

sheligalo

As far as C4 goes, then take the first comment, u=sint for the second integral

Reply 5

Muffin.

By inspection. Notice that you're integrating a function and its derivative

Reply 6

devan5

So will it be

4sin^3t

Thanks Tsr :woo:

devan5

Stuck on this one

By integration, find an exact value for the area

How would i integrate the second function, i dont seem to be getting anywhere with parts :s-smilie:

Can someone help me please

thanks

\int^\frac{\pi}{2}_\frac{\pi}{3} 9tsint dt - \int^\frac{\pi}{2}_\frac{\pi}{3}12sin^2tcostdt

the second equation you basically follow the chain rule (from differentiation) but in reverse.

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