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Let f denote an integral sign, I will write the integrand in square brackets. The formula for integration by parts is given by:f [(u)(dv/dx)]dx = uv - f [((du/dx)(v)]dxTo apply ...
First we need to use trigonometric identities to convert the sin^3(x) to a single power. This is because we cannot integrate trigonometric functions that are above the power of 1. We need to use the doubl...
We know that f'(x) = x^3 + 2*x^0.5 + 8, and we can integrate both sides. This gives us f(x) = (1/4)*x^4 + (4/3)x^(3/2) + 8x + c, remembering to add the constant of integration. Now, we are almost...
= (4/3)x3 - (10/2)x2 + x1/2/(1/2) + C = (4/3)x3 - 5x2 + 2x1/2 + C
The idea here is to pair your numbers up to get to the solution. If you were to put this through a calculator it would take you a while. However, if we simplify the problem to the sum of 1 to 10 you'll be...
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