Given 4∫8 (4 on top, 8 on bottom) f(x)dx= 12 and 4∫8 g(x)dx= 5.
Evaluate the following:
4∫8 [2f(x)-3g(x)]dx
Would I just put 12 in for f(c) and 5 in for g(x) then solve?
yes, but there's not much to solve at that point. Just evaluate the expression:
2*12 - 3*5
Alright thank you so much Steve.
To evaluate the integral 4∫8 [2f(x) - 3g(x)]dx, you cannot simply substitute the values of f(x) and g(x) given in the problem and solve. Instead, you need to use the properties of integrals to evaluate the expression.
Let's break down the integral step by step:
1. Start with 4∫8 [2f(x) - 3g(x)] dx.
2. Distribute the factor of 2 within the integral to both f(x) and g(x): 4∫8 (2f(x) - 3g(x)) dx.
3. Apply the linearity property of integrals: 4∫8 2f(x) dx - 4∫8 3g(x) dx.
4. Since we're given the definite integrals of f(x) and g(x), we can replace the integrals with their respective values: 4 * 12 - 4 * 5.
Now, evaluate the expression:
4 * 12 - 4 * 5
= 48 - 20
= 28.
Therefore, the value of the integral 4∫8 [2f(x) - 3g(x)] dx is 28.