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anonymous
 5 years ago
hey can someone please help me find the integral of sqrt of y^249. i know i have to use trig substitution but i need help with actually solving it
anonymous
 5 years ago
hey can someone please help me find the integral of sqrt of y^249. i know i have to use trig substitution but i need help with actually solving it

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}\sqrt{y^249}dy\] let \[\frac{y}{7}=\tan(\theta)\] \[\frac{dy}{7}=\sec^2\theta d \theta\] \[\int\limits_{}^{}\sqrt{(7\tan \theta)^249}7\sec^2\theta d \theta\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isnt it better to use 7 sin theta as a sunstitution

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[7\int\limits_{}^{}\sqrt{49}\sqrt{\tan^2\theta1}\sec^2(\theta)d \theta\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[7*7\int\limits_{}^{}\sec \theta*\sec^2(\theta) d \theta\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[49\int\limits_{}^{}\sec^3(\theta) d \theta\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1oops i made the wrong substitution

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1tan^2x+1=sec^2x not tan^2x1=sec^2x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could you do it using sin theta as the substitution if it not too much trouble

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is the part im stuck if it helps

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1you could also use sintheta=y/7

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then i knew i i got the integral of cos^2 theta which came out to ve 1/2 theta 1/4 cos 2 theta

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\sin \theta=\frac{y}{7}\] \[\cos(\theta)d \theta=\frac{dy}{7}\] \[(\sin \theta)^2=(\frac{y}{7})^2\] \[49\sin^2(\theta)=y^2\] \[\int\limits_{}^{}\sqrt{49\sin^2(\theta)49}*7\cos(\theta)d \theta\] \[7\int\limits_{}^{}\sqrt{49}*\sqrt{\sin^2(\theta)1}*\cos(\theta)d \theta=49\int\limits_{}^{}\cos^2\theta d \theta\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1remember cos^2(theta)=1/2*(1+cos(2theta))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[49*\frac{1}{2}\int\limits_{}^{}(1+\cos(2\theta)) d \theta=\frac{49}{2}*(\theta+\frac{1}{2}\sin (2\theta))+C\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1but remember sin(2theta)=2sin(theta)cos(theta)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\frac{49}{2} \theta+\frac{49}{2} \sin(\theta)\cos(\theta)+C\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1we need this in terms of x though we let sintheta=y/7 so costhetha=sqrt(49y^2)/7

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1also since sintheta=y/7 then theta=arcsin(y/7)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1meant in terms of y lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey i forgot to give you the limits bc i am having trouble plugging it its 0 to 7

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\frac{49}{2}\sin^{1} (y)+\frac{49}{2}\frac{y}{7}\frac{\sqrt{49y^2}}{7}+C\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\frac{49}{2}\sin^{1} (y)+\frac{y}{2}\sqrt{49y^2}+C \]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1you are having trouble plugging in?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1wherever you see a y plug in your upper limit then minus wherever you see a y plug in your lower limit

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[(\frac{49}{2}\sin^{1}(7)+\frac{7}{2}\sqrt{497^2})(\frac{49}{2}\sin^{1}(0)+\frac{0}{2}\sqrt{490^2})\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\frac{49}{2}\sin^{1}(7)\]
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