Question

HELPP ME!!!

Answer 1

Answer:

b=3.827

Step-by-step explanation:

Given that the area of the region under the curve of the function f(x) = 5x + 7 on the interval [1, b] is 88 square units, where b > 1.

Area of the curve above x axis under f(x) between a and b is given by

$\int\limits^a_b {5x+7} \, dx$

=$\int\limits^1_b {5x+7} \, dx$

=$\frac{5x^2}{2} +7x$

Substitute limits

Area = $5(b^2-1)+7(b-1)=88\\5b^2+7b-100=0\\b=3.827$

(Negative value b =-5.227 is ignored as given that b>1)

Answer 2

Answer:

b = -83/5

Step-by-step explanation:

So we know the integral of a function from a to b represents the area under the curve.  And we solve integrals subtracting the equation when plugging in a, from the equation when plugging in b.

We can write this into a formula like such:

(5 * 1 + 7) - (5b + 7) = 88

12 -5b - 7 = 88

5 - 5b = 88

5b = -83

b = -83/5