question 7 (1 point)\nsuppose $\\int_{-2}^{7}(3 f(x)) d x=12$ and $\\int_{5}^{7} f(x) d x=2$. compute…

question 7 (1 point)\nsuppose $\\int_{-2}^{7}(3 f(x)) d x=12$ and $\\int_{5}^{7} f(x) d x=2$. compute $\\int_{-2}^{5} f(x) d x$.\n4\n8\n10\n0\n2\nview hint for question 7

question 7 (1 point)\nsuppose $\\int_{-2}^{7}(3 f(x)) d x=12$ and $\\int_{5}^{7} f(x) d x=2$. compute $\\int_{-2}^{5} f(x) d x$.\n4\n8\n10\n0\n2\nview hint for question 7

Answer

Explanation:

Step1: Use the property of definite integral (\int_{a}^{b}kf(x)dx = k\int_{a}^{b}f(x)dx)

Given (\int_{-2}^{7}(3f(x))dx = 12), then (3\int_{-2}^{7}f(x)dx=12), so (\int_{-2}^{7}f(x)dx = 4)

Step2: Use the property of definite integral (\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx=\int_{a}^{c}f(x)dx)

We know that (\int_{-2}^{7}f(x)dx=\int_{-2}^{5}f(x)dx+\int_{5}^{7}f(x)dx) Since (\int_{-2}^{7}f(x)dx = 4) and (\int_{5}^{7}f(x)dx = 2) Substitute the values into the formula: (4=\int_{-2}^{5}f(x)dx + 2)

Step3: Solve for (\int_{-2}^{5}f(x)dx)

(\int_{-2}^{5}f(x)dx=4 - 2)

Answer:

(2)