Use the Second Fundamental Theorem of calculus combined with the Generalized Power Rule to evaluate the integral:
(integral from zero to pi/2) [(sin^2)3xcos3x(dx)]
I'm extremely lost in my calc class! Please help and show any work if possible!
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Anonymous
ANSWERS: 1
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I'm not sure what the "Second Fundamental Theorem of Calculus" is supposed to be. But the integral you mentioned looks like integral f(u) (du/dx) dx where du/dx is cos 3x In such a case, you can use the substitution rule, sometimes confusingly called the chain rule, which turns: integral (between x1 and x2) of f(u) (du/dx) dx into integral (between u1 and u2) of f(u) du where u is some function of x here if we have du/dx = cos 3x then u could be taken to be defined as u = sin 3x And your integral becomes: find the integral between sin(3*0) and sin(3*pi/2) of u^2 du which is much easier. (when you work this out, beware because the limits will look backwards: integral from a to b = - integral from b to a)
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