2_jenny_9
How do you integrate this using substitution ?
∫sin (3pi/2 + pi/4)dx



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

Mimi_x3
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I think it's missing a \(x\)

2_jenny_9
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yea thats the question

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

2_jenny_9
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the answer at the back is 2/3pi cos (3pi/2 + pi/4) +c

Mimi_x3
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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

2_jenny_9
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yea thats the question

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

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

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

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

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

baddinlol
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Then integrate sqrt(2)/2

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

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

2_jenny_9
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thank you :)