Find
\[\int \left(10x^4 - 4x - \frac{3}{\sqrt{x}} \right) dx\]
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 4 - 2013 - Paper 1
Question 4
Find
\[\int \left(10x^4 - 4x - \frac{3}{\sqrt{x}} \right) dx\]
giving each term in its simplest form.
Worked Solution & Example Answer:Find
\[\int \left(10x^4 - 4x - \frac{3}{\sqrt{x}} \right) dx\]
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 4 - 2013 - Paper 1
Step 1
Step 1: Integrate Each Term
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Answer
To integrate each term separately:
For the term 10x4:
[ \int 10x^4 , dx = 10 \cdot \frac{x^{5}}{5} = 2x^5 ]
For the term −4x:
[ \int -4x , dx = -4 \cdot \frac{x^{2}}{2} = -2x^2 ]
For the term −x3 (which can be rewritten as −3x−21):
[ \int -3x^{-\frac{1}{2}} , dx = -3 \cdot \frac{x^{\frac{1}{2}}}{\frac{1}{2}} = -6x^{\frac{1}{2}} ]
Step 2
Step 2: Combine the Results
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Answer
Combining all the integrated terms, we have:
[2x^5 - 2x^2 - 6\sqrt{x} + C]
where C is the constant of integration.
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