Evaluate the definite integral below.∫42(8+7e−1.9x)dx∫24(8+7𝑒−1.9𝑥)d𝑥Enter your answer in exact form or rounded to two decimal places.Answer

To solve the definite integral ∫ from 2 to 4 (8+7e^(-1.9x)) dx, we need to find the antiderivative (also known as the integral) of the function and then apply the Fundamental Theorem of Calculus.

The antiderivative of a constant, like 8, is just 8x.

The antiderivative of 7e^(-1.9x) is a bit more complicated. We can use the rule ∫e^(ax) dx = (1/a)e^(ax) to find that the antiderivative of 7e^(-1.9x) is -(7/1.9)e^(-1.9x).

So, the antiderivative of our function is F(x) = 8x - (7/1.9)e^(-1.9x).

Now, we apply the Fundamental Theorem of Calculus, which says that the definite integral from a to b of a function is F(b) - F(a), where F is the antiderivative of our function.

So, ∫ from 2 to 4 (8+7e^(-1.9x)) dx = F(4) - F(2) = [84 - (7/1.9)e^(-1.94)] - [82 - (7/1.9)e^(-1.92)].

Now, you just need to calculate these values and subtract to get the answer.