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Find \[\int (8x^3 + 4) \, dx\] giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2014 - Paper 1

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$Find-\[\int-(8x^3-+-4)-\,-dx\]-giving-each-term-in-its-simplest-form.-Edexcel-A-Level Maths Pure-Question 3-2014-Paper 1.png$

Find \[\int (8x^3 + 4) \, dx\] giving each term in its simplest form.

Worked Solution & Example Answer:Find \[\int (8x^3 + 4) \, dx\] giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2014 - Paper 1

Step 1

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Answer

To find the integral of (8x^3), we apply the power rule of integration:

[\int x^n , dx = \frac{x^{n+1}}{n+1} + C]

Thus,

[\int 8x^3 , dx = 8 \cdot \frac{x^{3+1}}{3+1} + C = 8 \cdot \frac{x^4}{4} + C = 2x^4 + C]

Step 2

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Answer

For the integral of a constant, we have:

[\int c , dx = cx + C]

So,

[\int 4 , dx = 4x + C]

Step 3

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Answer

Combining the results from the two parts:

[\int (8x^3 + 4) , dx = 2x^4 + 4x + C]

Here, (C) is the constant of integration.

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