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Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: $\int_a^bf(x)dx=-\int_b^af(x)dx$
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$-\int_{1}^{6}\sqrt{x}\left(3x^2-2\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function x^1/2(3x^2-2) from 6 to 1. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. Rewrite the integrand \sqrt{x}\left(3x^2-2\right) in expanded form. Expand the integral \int\left(3\sqrt{x^{5}}-2\sqrt{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral of a function times a constant (3) is equal to the constant times the integral of the function.