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Integration (OCR A Level Maths: Pure)
Exam Questions
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This topic pack contains questions on the following:
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Fundamental Theorem of Calculus
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Integrating Powers of x
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Definite Integration
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Indefinite Integration
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Area Under a Curve
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Area between a Curve and a Line
Use calculus to find
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Evaluate
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Find the equation of the curve passing through the point (4, 64) and given by
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Show that
Hence, or otherwise, work out
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Given
find the value of the positive constant k.
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The diagram below shows part of the graph of
Write down the values of x where .
Show that
Evaluate
Write down the area of the region labelled R.
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Given and that when ,, show that
Find an equation for y in terms of x, given that when , .
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The diagram below shows part of the graph of .
Find the area of the shaded region labelled R.
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Find the x-coordinates of the intercepts of the line with equation and the curve with equation
Evaluate
The diagram below shows the graphs of and .
Find the exact area of the shaded region R.
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The diagram below shows the graphs of the line and the curve
Work out the x-coordinates of the points labelled P, Q and R.
Work out the area of the shaded region.
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Use calculus to find
Write down
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Use calculus to find the value of
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Find the equation of the curve passing through the point (-2, 3) and given by
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Using the binomial expansion, or otherwise, show that
Hence, or otherwise, work out
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Given
find the value of the constant p, where .
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The diagram below shows part of the graph of
Find the area of the shaded region labelled R.
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A function,, has second derivative given by
Given that , and find
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The diagram below shows part of the graph of .
Find the total area of the two shaded regions.
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The line with equation cuts the curve with equation at the points P and Q, as shown.
Find the x- and y-coordinates of the points P and Q.
Find the exact area of the region labelled R, giving your answer in the form , where a and b are integers to be found.
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The diagram below shows the graphs of and
Find the exact area of the shaded region.
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Use calculus to find
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Use calculus to find the value of
giving your answer correct to 3 significant figures.
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Find the equation of the curve passing through the point (4, -8) and given by
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Show that
Hence, or otherwise, work out
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Given
find the value of the constant q.
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The diagram below shows part of the graph of
Find the area of the shaded region labelled R.
Without doing any additional calculation, explain why must be equal to zero.
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A function, , has second derivative given by
Given that and are factors of , find .
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The diagram below shows part of the graph of
Find the total area of the two shaded regions.
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The diagram below shows the graphs of and .
Find the exact area of the shaded region.
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The diagram below shows the graphs of and .
Find the total area of the shaded regions.
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