(1 point) Let ??² f(x) dx = 5, ??³ f(x) dx = 9, ??² g(x)...

(1 point) Let ??² f(x) dx = 5, ??³ f(x) dx = 9, ??² g(x) dx = 1, ??³ g(x) dx = -15, Use these values to evaluate the given definite integrals. a) ??² (f(x) + g(x)) dx = b) ??³ (f(x) - g(x)) dx = c) ??³ (3f(x) + 2g(x)) dx = d) Find the value a such that ??³ (af(x) + g(x)) dx = 0. a =

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 In this question, we're given the values of several integrals, and using these values, we're asked to calculate some other values.

00:10 So first of all, given integrals f of x and g of x from 0 to 2, we're asked to calculate interval of f of x plus g of x from 0 to 2.

00:21 Now using linearity of integrals, we can rewrite this as integral from 0 to 2, f, dx, plus integral from 0 to 2, g, dx.

00:33 And since we know the value of inch integral, so integral f from 0 to 2 is 5, and integral of g from 0 to 2 is 1, we find that the sum is equal to 6.

00:55 Now in the second part, we are asked to find integral from 0 to 3, f minus g.

01:10 Now let's, so we are given integral of f from 0 to 3.

01:15 However, we are not given integral of g from 0 to 3, but we can easily obtain it by summing integrals from 0 to 2 and 2 to 3 of g.

01:27 So, we can rewrite this as integral from 0 to 3 f of x d x minus integral from 0 to 3 g of x d x.

01:41 And we are given that the value of f is 9.

01:46 This is equal to 9.

01:48 Now the value of the integral of g from 0 to 3 is integral of g from 0 to 2 plus integral of g from 2 to 3.

02:07 And that's going to be 1 minus 15.

02:15 So it's negative 14.

02:18 Therefore, the total integral is going to be 9 minus negative 14.

02:29 And that's going to be 14 plus 9, which is 23...

Question

(1 point) Let ??² f(x) dx = 5, ??³ f(x) dx = 9, ??² g(x) dx = 1, ??³ g(x) dx = -15, Use these values to evaluate the given definite integrals. a) ??² (f(x) + g(x)) dx = b) ??³ (f(x) - g(x)) dx = c) ??³ (3f(x) + 2g(x)) dx = d) Find the value a such that ??³ (af(x) + g(x)) dx = 0. a =

Please give Ace some feedback