How do you find \int _ { - 2} ^ { 0} ( 2x + 5) d x?

2 Answers
Mar 2, 2017

6 units squared.

Explanation:

Using the chain rule, the integral is int_-2^0 x^2 + 5x dx

=x^2+5x]_-2^0 So we have to evaluate at the upper limit and evaluate the bottom limit and subtract them.

(0)^2+5*(0) = upper limit = 0

(-2)^2+5*(-2) = bottom limit = -6

Thus the answer is 0-(-6) = 6 units squared.

Mar 3, 2017

int_(-2)^0 \ 2x + 5 \ dx = 6

Explanation:

graph{2x+5 [-9.58, 10.42, -2.52, 7.48]}

The integrand is y=2x+5,and the integral represents the area under the curve from x=2 to x=0

With y=2x+5:

x=0 \ \ \ \ \=> y=5
x=-2 => y=1

The area is a trapezium with w=2, a=1, b=5#

Hence,

int_(-2)^0 \ 2x + 5 \ dx = 1/2(5+1)(2) = 6