MATH SOLVE

4 months ago

Q:
# Continuous functions f, g are known to have the properties z 4 1 f(x) dx = 19, z 4 1 g(x) dx = 12 respectively. use these to find the value of the integral i = z 4 1 (8f(x) β g(x) + 7) dx. 1. i = 157 2. i = 161 3. i = 159 4. i = 163 5. i = 155

Accepted Solution

A:

I guess this reads[tex]\displaystyle\int_1^4f(x)\,\mathrm dx=19[/tex][tex]\displaystyle\int_1^4g(x)\,\mathrm dx=12[/tex]You want to compute[tex]I=\displaystyle\int_1^4(8f(x)-g(x)+7)\,\mathrm dx[/tex]By linearity of the definite integral,[tex]I=\displaystyle8\int_1^4f(x)\,\mathrm dx-\int_1^4g(x)\,\mathrm dx+7\int\mathrm dx[/tex][tex]I=8\cdot19-12+7(4-1)=\boxed{161}[/tex]