AP Calculus ABhardmcq1 pt

If 15f(x)dx=12\int_1^5 f(x)\,dx=12 and 35f(x)dx=7\int_3^5 f(x)\,dx=7, what is the value of 51f(x)dx+13f(x)dx\int_5^1 f(x)\,dx+\int_1^3 f(x)\,dx?

A.7-7
B.77
C.5-5
D.55

Explanation

Core Concept

First, 13f=15f35f=127=5\int_1^3 f=\int_1^5 f-\int_3^5 f=12-7=5. Then 51f=12\int_5^1 f=-12, so the sum is 12+5=7-12+5=-7.

Correct Answer

A7-7

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