Mathematics 82 Online
OpenStudy (anonymous):

my question is: cos^2 x = ???

OpenStudy (anonymous):

what are you finding?

OpenStudy (anonymous):

I want to find " integral 16 cos^2 x

OpenStudy (anonymous):

oh ok

OpenStudy (anonymous):

Let me see.

OpenStudy (anonymous):

Let me see.

OpenStudy (anonymous):

8(x+sin(x)cos(x))

OpenStudy (anonymous):

ahaa.. SURE !!? My teacher will kill me hahaha

OpenStudy (anonymous):

cos2x = 2cos square X -1

OpenStudy (anonymous):

so cos square X = (1+cos2X)/2

OpenStudy (anonymous):

srinu7j ; not cos 2x ... its( cos ^2) x

OpenStudy (anonymous):

Let me see.

OpenStudy (anonymous):

yeah

OpenStudy (agreene):

$\int16cos^2(x)dx$ $=16 \int cos^2(x) dx$ $= 16 \int (1/2 cos(2 x)+1/2) dx$ $= 16 \int 1/2 dx + 8 \int cos(2 x) dx$ For the integrand cos(2 x), substitute u = 2 x and du = 2 dx: $= 4 \int cos(u) du+16 \int 1/2 dx$ $= 4 \int cos(u) du+8 x$ $= 4 sin(u)+8 x+c$ Substitute back for u = 2 x: $= 8 x+4 sin(2 x)+c$ $\huge = 8 (x+sin(x) cos(x))+c$

OpenStudy (anonymous):

I will repate my Q: INTEGRAL 16 cos^2|dw:1319605597473:dw| x