# Find the integral between 4 and 1 of x^(3/2)-1 with respect to x

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When we integrate a function we must first raise the power of x in each term by one. The first term therefore becomes x^(5/2). The second term can be thought of as x^0 which we know that any number to the power zero is equal to 1, so the second term becomes x. We must then divide by the new power of x. In the first term we have 1 divided by 5/2 which is equal to 2/5 and in the second term we have -1 divided by 1 which is still equal to -1. Because the integral has limits we do not need to include an integration constant. The integrated expression is (2/5)x^(5/2) - x. The next step in solving this problem is to substitute the limits into the equation. What we do here is take away the value of our integrated function at the lower bound from the value of the integrated function at the upper bound. This gives us the calculation ((2/5) x 4^(5/2) - 4) - ((2/5) x 1^(5/2) - 1). This can be evaluated on your calculator to give 9.4.

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