For a continuous function

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

For a continuous function pp, it is known that ∫17p(x) dx=2\displaystyle\int_{1}^{7} p(x)\,dx=2 and ∫47p(x) dx=−5\displaystyle\int_{4}^{7} p(x)\,dx=-5. If p(x)≥0p(x)\ge 0 on [1,4][1,4], find ∫14p(x) dx\displaystyle\int_{1}^{4} p(x)\,dx.

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