Question

Given that f24=−5∫24​f(x)dx=−5, ∫27=3∫27​f(x)dx=3, and ∫27=7∫27​g(x)dx=7, evaluate the following integral:

∫27=∫27​g(x)dx

Answer 1

The value of the integral ∫_2^7 g(x) dx is given directly in the question and it is 7. There is no need for further calculations since the same integral has been evaluated.

Step-by-step explanation:

Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives.

To evaluate the integral ∫_2^7 g(x) dx, we can use the information provided for ∫_2^7 g(x) dx = 7. Since this is the same integral that is being asked to evaluate, we already have the answer given to us in the question. Therefore, the value of the integral ∫_2^7 g(x) dx is 7.