Question Video: Finding the Integration of a Function Using the Power Rule for Integration with a Negative Exponent | Nagwa Question Video: Finding the Integration of a Function Using the Power Rule for Integration with a Negative Exponent | Nagwa

Question Video: Finding the Integration of a Function Using the Power Rule for Integration with a Negative Exponent Mathematics • Second Year of Secondary School

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Determine β« β(2/7)π₯β»βΉ dπ₯.

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Video Transcript

Determine the indefinite integral of negative two over seven multiplied by π₯ to the power of negative nine with respect to π₯.

In our integral, we simply have a power function. So we can use the power rule for integration in order to find this integral. It tells us that the indefinite integral of π₯ to the power of π with respect to π₯ is equal to π₯ to the power of π plus one over π plus one plus πΆ. In our case, weβre integrating negative two-sevenths π₯ to the power of negative nine with respect to π₯. So our power of π₯ is negative nine. We can start by writing down our constant which is negative two-sevenths.

Then since our value of π is negative nine, we next need to write π₯ to the power of π plus one over π plus one. So thatβs π₯ to the power of negative nine plus one which is π₯ to the power of negative eight over negative nine plus one. So thatβs negative eight. Then we mustnβt forget to add our constant of integration πΆ. For our final step here, we just need to simplify. And we obtain our solution which is that the indefinite integral of negative two-seventh multiplied by π₯ to the power of negative nine with respect to π₯ is equal to π₯ to the power of negative eight over 28 plus πΆ.

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