Question

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) − g(x) + 7) dx. 1. i = 157 2. i = 161 3. i = 159 4. i = 163 5. i = 155

Answer 1

I guess this reads

$\displaystyle\int_1^4f(x)\,\mathrm dx=19$

$\displaystyle\int_1^4g(x)\,\mathrm dx=12$

You want to compute

$I=\displaystyle\int_1^4(8f(x)-g(x)+7)\,\mathrm dx$

By linearity of the definite integral,

$I=\displaystyle8\int_1^4f(x)\,\mathrm dx-\int_1^4g(x)\,\mathrm dx+7\int\mathrm dx$

$I=8\cdot19-12+7(4-1)=\boxed{161}$