Question

How do you integrate this using substitution ?
∫sin (3pi/2 + pi/4)dx

Answer 1

\[\large\int \sin (\frac{3\pi}{2} +\frac{\pi}{4})dx?\]

Answer 2

I think it's missing a \(x\)

Answer 3

yea thats the question

Answer 4

Would the answer be sqrt(2)/2 x?

Answer 5

the answer at the back is -2/3pi cos (3pi/2 + pi/4) +c

Answer 6

Are you sure that it's \[\int sin\left(\frac{3\pi}{2}+\frac{\pi}{4}\right)
dx\]??
I think that it's missing a \(x\) somewhere

Answer 7

yea thats the question

Answer 8

Ok so the answer is -sqrt(2)/2 x

Answer 9

Just simplify sin ( (3pi/2) + (pi/4))

Answer 10

sin ((3pi/2) + (pi/4)) = -sin(pi/4)

Answer 11

Then if you remember your exact values, sin(pi/4) = sqrt(2)/2

Answer 12

So -sin(pi/4) = -sqrt(2)/2

Answer 13

Then integrate sqrt(2)/2

Answer 14

I mean integrate -sqrt(2)/2 with respect to x

Answer 15

You will get integral(sin ( (3pi/2) + (pi/4))) = -sqrt(2)/2 x

Answer 16

thank you :)