Hi everyone! On friday's class we learned all about the method of substitution.

There are 3 main steps to this method:

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1. SUBSTITUTE:

-you let the inner function g(x) = u
-differentiate that inner function and let it = du/dx
-we solve for du by multiplying dx to the other side (cross multiply):
eg.
du = 3
dx
du = 3dx
-substitute u and du in original given integral.

2. ANTIDIFFERENTIATE:

-antidifferentiate the new integral that consist of u and du.

3.RESUBSTITUTE:

-substitute g(x) the inner function in for u to get your final answer, an antiderivative.

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*REMEMBER: It doesn't hurt to check your final answer by differentiating!!!


If it matches the given integral then your answer is right!!!

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The following examples we did in class will show and explain this method:

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1) the integral of sin (3x) dx


Click--> on pic so it's easier to read

ANSWER: -1/3 cos(3x) + C

*DON'T FORGET + C











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2) the integral of 5e^5x dx

Click--> on pic so it's easier to read

ANSWER: e^5x + C

*DON'T FORGET + C

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3) the integral of (x^3+2)^4 ( 3x^2) dx

Click--> on pic so it's easier to read

Answer: (x^3+2)^5 / 5 + C

*DON'T FORGET + C.

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3) the integral of (x^3+2)^4 ( x^2) dx

- similar to question #3 but WITHOUT the 3 in front of x^

Click--> on pic so it's easier to read

Answer: (x^3+2)^5 / 15 + C

*DON'T FORGET + C.

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4) the integral of (x / √x+7 ) dx

Click--> on pic so it's easier to read

Answer: 2/3(x+7)^3/2 - 14(x+7)^1/2 + C

*DON'T FORGET + C.

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HOMEWORK: 7.3 Exercises --> odd #'s

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The next scriber is MARK =]