What is the Integral of 1/2(1+cos(theta))^2 ?
Is it the same as finding the integral of 1/2(1+2cos(theta)+cos^2(theta)) ?
Thanks in advance,
Is it the same as finding the integral of 1/2(1+2cos(theta)+cos^2(theta)) ?
Thanks in advance,
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Yes, it is
(1/2) * dt + cos(t) * dt + (1/2) * cos(t)^2 * dt
(1/2) * dt + cos(t) * dt + (1/2) * (1/2) * (1 + cos(2t)) * dt
(1/2) * dt + cos(t) * dt + (1/4) * dt + (1/4) * cos(2t) * dt
(3/4) * dt + cos(t) * dt + (1/4) * cos(2t) * dt
Integrate
(3/4) * t + sin(t) + (1/8) * sin(2t) + C
(1/2) * dt + cos(t) * dt + (1/2) * cos(t)^2 * dt
(1/2) * dt + cos(t) * dt + (1/2) * (1/2) * (1 + cos(2t)) * dt
(1/2) * dt + cos(t) * dt + (1/4) * dt + (1/4) * cos(2t) * dt
(3/4) * dt + cos(t) * dt + (1/4) * cos(2t) * dt
Integrate
(3/4) * t + sin(t) + (1/8) * sin(2t) + C
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The first integral is equal to 1/8 (6x + 8sin(X) + sin(2x)) and plus a constant for indefinite integral.
The second integral is the same!
I have a really cool link I want to share with you, it is how I did these integrals really quickly, and I often use it when I'm using calculus just to check my work.
Its on wolframalpha.com .... A friend of mine showed it to me.. all you have to do is take the description of your integral, like " Integral of 1/2(1+cos(theta))^2 " and type it in just like that and it will do the math for you, and give plots of the curve, alternate forms of the integral etc.. it is really useful!
The second integral is the same!
I have a really cool link I want to share with you, it is how I did these integrals really quickly, and I often use it when I'm using calculus just to check my work.
Its on wolframalpha.com .... A friend of mine showed it to me.. all you have to do is take the description of your integral, like " Integral of 1/2(1+cos(theta))^2 " and type it in just like that and it will do the math for you, and give plots of the curve, alternate forms of the integral etc.. it is really useful!