Evaluate ∫(1)/(√(x))sec(√(x) - 1) tan(√(x)

Evaluate $\int \frac{1}{\sqrt{x}} \sec(\sqrt{x} - 1) \tan(\sqrt{x} - 1) dx$. Select one: a. $\frac{1}{2} \sec(\sqrt{x} - 1) + C$ b. $\sec(\sqrt{x} - 1) + C$ c. $-2 \sec(\sqrt{x} - 1) + C$ d. $2 \sec(\sqrt{x} - 1) + C$

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Transcript

00:01 Let's evaluate this definite integral of x times of e power x squared plus 2.

00:07 And the limits are from x equal to 0 to x equal to 1.

00:11 So i'm going to evaluate this definite integral using substitution method.

00:16 That is, i'm going to substitute this x squared as u.

00:21 So let's do that.

00:23 Let's put x squared equals u.

00:25 Now we take the derivative on both sides.

00:28 The derivative of x squared using power rule is 2x times dx and this equals the derivative of u is d u let's solve for x dx we have x d x and this equals d u over 2 we solve this specifically for x d x because we have x and d x these two are product which means that we can replace that as d u over 2 so let's apply the substitution and so so therefore this different integral will become integral from x dx is du by 2.

01:04 I write this as du by 2 for x times of d x.

01:09 And then e to the power replace x squared by u.

01:12 So this will become e power u and then plus 2.

01:16 I'm just finding the indefinite integral.

01:19 I'm not writing the limits because we will have to integrate this first with respect to you and then apply the same limit of x.

01:28 After doing the back substitution of you.

01:30 So let's evaluate this indefinite integral...

Question

Evaluate $\int \frac{1}{\sqrt{x}} \sec(\sqrt{x} - 1) \tan(\sqrt{x} - 1) dx$. Select one: a. $\frac{1}{2} \sec(\sqrt{x} - 1) + C$ b. $\sec(\sqrt{x} - 1) + C$ c. $-2 \sec(\sqrt{x} - 1) + C$ d. $2 \sec(\sqrt{x} - 1) + C$

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