Help Needed in Calculus

[aklemalp]

Well I'm currently doing calculus and is kind of stuck with the trigonometric substitution section. I want to know if any one of the members could drop in their two cents, so me or any one else could have a different perspective and a better insight into the this area of mathematics. Thank you. Your input is deeply acknowledged.

[godzilla]

Originally Posted by aklemalp
Well I'm currently doing calculus and is kind of stuck with the trigonometric substitution section. I want to know if any one of the members could drop in their two cents, so me or any one else could have a different perspective and a better insight into the this area of mathematics. Thank you. Your input is deeply acknowledged.

What do you need help with? When i did calculus, I used to use patrikjmath (a math youtuber) for any help. Believe me, he will teach you with in minutes. I think he is the best free help around - video wise.

[aklemalp]

^^thanks, will definitely try him. My professor recommended khan academy. But I don't understand thoroughly his method

[BengaliPagol]

i loved trig substitution questions

[aklemalp]

^loved is a strong word

[Neel Here]

would be glad to help. what exactly you need to know ?

[godzilla]

Yea khan academy is not that great as everyone makes it seem. But for calculus if you're not to fimilar with trigonometry in general, try to memorize them. Sin cos tan are the usual ones.

[aklemalp]

Integrate(16-4x^2)dx. This one have been giving me a hard time. I tried 27 seven times and all attempts I was wrong.

[tonoy]

are you sure that's the problem?

= 16x- (4x^3/3)
=4(4x-(x^3/3))+C

[aklemalp]

^^Oh,i forgot to put the expression under the square root. Sorry.

[godzilla]

Originally Posted by aklemalp
^^Oh,i forgot to put the expression under the square root. Sorry.

u substitution.

[aklemalp]

It's a Trig Substitution Question.

[tonoy]

let a = 2
x=2sin t; and then dx= 2cos t dt
so the orighinal equation will be
int sqrt(16- 4(2sin t)^2) 2 cos t dt
= int sqrt(16-16sin^2 t)(2cos t) dt
=int sqrt(16(1-sin^2 t)(2cos t) dt ...you can see that 1-sin^2 is cos^2
=int sqrt(16cos^2 t)(2 cos t) dt
=int (4cos t)(2cos t) dt
=int 8cos^2 t dt ... use trig identity where cos^2= (1/2) + (cos 2t/2)
=int 8((1/2) + ((cos 2t)/2)) dt
=int 4 + 4cos 2t dt
= 4t + 4((sin 2t)/2)
=4t + 2sin 2t..... sin2t= 2sin t cos t
=4t + 4(sin t cos t)
now all you have to do is resubstitute the t for x. where x= 2sin t, or sin t = x/2

if you draw a right triangle; where t is the angle, x would be the opposite, 2 would be the hypotnuse and sqrt(4-x^2) would be the adjacent

= 4(arcsin(x/2)) +4((x/2)(sqrt(4-x^2)/2))
=4arcsin(x/2) + x(sqrt(4-x^2) + C

[aklemalp]

^^ Thanks alot bro. I just entered it and wrong. I think that they're looking for a solution with the Natural Log in it. Some part of it is going to be absorbed into the Constant. Atleast that was what one of the tutors implied.

[tonoy]

are you sure the problem was integration of sqrt(16-4x^2) dx?

[aklemalp]

Oh god, I've so much of a rough time with problem that I have entered the wrong one. I copy and pasted the correct problem below:

Evaluate the integral \int \sqrt{16 + 4 x^2} \, dx using trigonometric substitution.

I am so sorry bro for the wrong information.

[aklemalp]

Guys, Members,some help here please. I have a question that asking me to find the integral of sin(x^2). It's not 1-cos^2 x.

[Zeeshan]

Google renders studying Calculus useless.

[aklemalp]

^^Everytime someone types toy into the google search bar it automatically suggests adults toys.Google is not the perfect tool. Zeeshan, I sense your sarcasm but it will not be applicable in my situation.

[aklemalp]

Need some help with Improper Integrals:
Question : Integrate 1/(x-e^(-x)) from 3 to infinity. Thanks in advance.

[aklemalp]

Question: Convert (xy)^{2}=4 to an equation in polar coordinates.

Note: use "t" for \theta

[al Furqaan]

Originally Posted by tonoy
are you sure that's the problem?

= 16x- (4x^3/3)
=4(4x-(x^3/3))+C

That can be further factored to

4x(4-x^2/3) + C