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# Evaluate each definite integral.$$\int_{0}^{4}-\left(3 x^{3 / 2}+x^{1 / 2}\right) d x$$

## $-\frac{656}{15}$

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

I don't know. We have the definite integral zero two four of minus X to the three halves plus x to the one half d x. I could start by finding an anti derivative. So we have so this minus Khun stay are here. And then the entire derivative is so we add one to the exponents We get X to the five hands over five hands plus x to the three halves over three. House evaluated from zero to four. Okay. And so four to the five halves We'LL take the square root and then take the fifth power. So it's two to the fifth, which he be thirty two over five halves plus okay. Squared two cubes of eight over three halves and then minus this evaluated your over that Syria. Okay, so, uh, this is minus can multiply by their sim prickles of both the numerator is get doubles at sixty for over five plus sixteen over three and so we need to get a common denominator. I mean, we could leave it like this, but if we do get the common denominator of fifteen, you should get negative. Six fifty six. Divided by fifteen is the final answer

Georgia Southern University
##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp