1-6 Evaluate the integral by making the given...

1-6 Evaluate the integral by making the given substitution. 1. ? cos 2x dx, u = 2x 2. ? x(2x^2 + 3)^4 dx, u = 2x^2 + 3 3. ? x^2 ?(x^3 + 1) dx, u = x^3 + 1 4. ? sin^2 ? cos ? d?, u = sin ? 5. ? x^3 / (x^4 - 5)^2 dx, u = x^4 - 5

Transcript

00:01 Hello everyone.

00:02 We are asked to evaluate the integral using the substitution method and we are given a specific u which we need to choose.

00:11 So first of all, the first question is integral cosine 2x d x and we need to choose u is equal to 2x.

00:20 So when u is equal to 2x, this implies that du is going to be 2dx and this implies that d u is going to be 2 dx and this implies that dx is is equal to d u divided by 2.

00:38 Now let's change the integral that is going to be integral cosine u d u divided by 2 and this is going to be 1 divided by 2 sine you.

00:53 We need to change u to 2 x that is going to be sine 2x divided by now let's move on to the second question we are given u as 2 x square plus 3.

01:10 So from u, d u will be equal to 4x d x which implies that d x is equal to d u divided by 4x.

01:27 Now the integral becomes x into u part 4 and instead of d x i need to write d u by 4x and now x and x gets cancelled.

01:40 So we'll be getting 1 divided by 4, u power 5 divided by 5.

01:48 Now change u back to 2x square plus 3.

01:52 That is going to be 2x square plus 3, the whole power 5 divided by 20.

02:00 The third question is we are given you to be x cube plus 1.

02:13 So d u will be 3 x squared d x and this implies that dx is equal to.

02:23 2, du, divided by 3, x squared.

02:27 Let's change the integral.

02:29 Integral now becomes x square, root u, du, divided by 3 x square...

Question

1-6 Evaluate the integral by making the given substitution. 1. ? cos 2x dx, u = 2x 2. ? x(2x^2 + 3)^4 dx, u = 2x^2 + 3 3. ? x^2 ?(x^3 + 1) dx, u = x^3 + 1 4. ? sin^2 ? cos ? d?, u = sin ? 5. ? x^3 / (x^4 - 5)^2 dx, u = x^4 - 5

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