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Problem For any continuous function g g g [ p , q ] [p,q] [ p , q ] ( p < q ) (p<q) ( p < q ) ∫ q p g ( x ) d x = ∣ ∫ p q g ( x ) d x ∣ \displaystyle \int_{q}^{p} g(x)\,dx = \left|\int_{p}^{q} g(x)\,dx\right| ∫ q p g ( x ) d x = ∫ p q g ( x ) d x ∫ q p g ( x ) d x = − ∫ p q g ( x ) d x \displaystyle \int_{q}^{p} g(x)\,dx = -\int_{p}^{q} g(x)\,dx ∫ q p g ( x ) d x = − ∫ p q g ( x ) d x ∫ q p g ( x ) d x = ∫ p q g ( x ) d x \displaystyle \int_{q}^{p} g(x)\,dx = \int_{p}^{q} g(x)\,dx ∫ q p g ( x ) d x = ∫ p q g ( x ) d x ∫ q p g ( x ) d x = 1 2 ∫ p q g ( x ) d x \displaystyle \int_{q}^{p} g(x)\,dx = \dfrac{1}{2}\int_{p}^{q} g(x)\,dx ∫ q p g ( x ) d x = 2 1 ∫ p q g ( x ) d x Browse the problem library