Question 7 (1 point)
Suppose $\int_{-2}^{7}(3 f(x)) d x=12$ and $\int_{5}^{7} f(x) d x=2$. Compute $\int_{-2}^{5} f(x) d x$
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D View hint for Question 7
Answer
Final Answer: The integral of \(f(x)\) from -2 to 5 is \(\boxed{2}\).
Step 1 ：The integral of a function from a to b is the area under the curve of the function from a to b. The integral of \(3f(x)\) from -2 to 7 is given as 12. This means that the integral of \(f(x)\) from -2 to 7 is \(12/3 = 4\).
Step 2 ：The integral of \(f(x)\) from 5 to 7 is given as 2.
Step 3 ：To find the integral of \(f(x)\) from -2 to 5, we can subtract the integral of \(f(x)\) from 5 to 7 from the integral of \(f(x)\) from -2 to 7.
Step 4 ：Subtracting, we get \(4 - 2 = 2\).
Step 5 ：Final Answer: The integral of \(f(x)\) from -2 to 5 is \(\boxed{2}\).
