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anhard
Sep 03, 2019

Integral examples

in Math Problems

I have some struggle to find sound solutions for these integrals.

It would give me much easier to comprehend what I have done wrong.


Thank you in advance.

Best regards

Anhard



Example 1




Example 2




Example 3




Example 4

Can use the substitution x= a tan(theta) or x= a sin(theta)

8 comments
Phinehas
Sep 04, 2019

I can do #2 if that helps, not sure about the others. I used u=3x and the D I method and got 1/9*(sin(u)-ucos(u))-2/3*cos(u)+c

Phinehas
Sep 04, 2019

Which is

when plugging in all the x's.

anhard
Sep 09, 2019

Thank you Phinehas. I think I forgot to substitute it frist. I will rewatch this example.

Louis Romao
Sep 04, 2019

#4 Use x=3sin(theta).

dx=3cos(theta) dtheta.


Substituting back:

sin(theta)=x/3

tan(theta)=x/sqrt(9-x^2)

Phinehas
Sep 04, 2019

Don't understand what you're saying about integration by parts, if you do that u-sub you're done at least when I did it. The answer is 5/9*(sin(10)-sin(7))

Aneesh Srinivas
Jun 23, 2020

my answer to number 3




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