The continuous function is defined on

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

The continuous function gg is defined on [0,12][0,12]. Selected values of definite integrals of gg are given below. ∫04g(x) dx=10,∫49g(x) dx=−6,∫912g(x) dx=5.\displaystyle \int_{0}^{4} g(x)\,dx=10, \qquad \int_{4}^{9} g(x)\,dx=-6, \qquad \int_{9}^{12} g(x)\,dx=5. (a) Calculate ∫012g(x) dx\displaystyle \int_{0}^{12} g(x)\,dx. Show all work. (b) Evaluate ∫012(2g(x)+3) dx\displaystyle \int_{0}^{12}\bigl(2g(x)+3\bigr)\,dx. Explain your steps clearly. (c) Compute the average value of gg on the interval [0,12][0,12]. State the units of your answer, if any.

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