Evaluate int01 x21e xdx 1 evaluate int01 x2 1e x dx 95712

Name: evaluate int01 x21e xdx 1 evaluate int01 x2 1e x dx 95712
Uploaded: 2023-10-26T05:39:20-08:00
Duration: 4 min 38 s
Channel: Khushbu Rani
Description: evaluate int01 x21e xdx 1 evaluate int01 x2 1e x dx 95712

Transcript

00:01 Hi, there is a question, you say that i need to integrate from 0 to 1 x square plus 1 e raised to the power minus x dx.

00:13 So, this is a clear case of integration by part.

00:18 So, let us first separate it out x square e raised to the power minus x dx plus e raised to the power minus x dx, let us say i equal to i1 plus i2.

00:32 This has definite, this is definitely the easiest calculation to do because its integration is coming out to be e raised to the power minus x plus c, but 0 to 1, so that means c will not be included, we will be looking it afterwards.

00:51 Let us first concentrate on i1 and equation number 1, i will be writing this.

00:58 I1 is 0 to 1 x square e raised to the power minus x dx.

01:04 Now, using integration by parts, this is first function, this is second function.

01:13 So, according to integration by part, it will be 0 to 1 first function integration of second function minus integration of differentiation of first function, integration of second function and whole integration.

01:35 This is first function, this is the second function.

01:42 So, from 0 to 1 x square integration of this is minus e raised to the power minus x minus its differentiation is 2x and its integration is same, so it will be plus e raised to the power minus x, 2 will be taken out and dx.

02:02 Again, from 0 to 1 minus x square e raised to the power minus x plus 2, again this is first function, this is the second function...

Question

Evaluate \int_0^1 (x^(2)+1)e^(-x)dx. 1. Evaluate $$\int_{0}^{1} (x^2 + 1)e^{-x} dx.$$

Question

Evaluate \int_0^1 (x^(2)+1)e^(-x)dx. 1. Evaluate $$\int_{0}^{1} (x^2 + 1)e^{-x} dx.$$

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