For a continuous function

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For a continuous function ff, let g(x)=∫0xf(t) dtg(x)=\int_{0}^{x} f(t)\,dt. You are given g(3)=8g(3)=8, g(12)=−2g(12)=-2, and ∫37f(t) dt=−5\displaystyle \int_{3}^{7} f(t)\,dt=-5. What is the value of ∫712f(t) dt\displaystyle \int_{7}^{12} f(t)\,dt? (a) −15-15 (b) 1010 (c) −5-5 (d) 55

Related theory

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