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.
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Given that show that
Hence find an expression in terms of x for the integral
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Given the identity , show that
Hence find the exact value of
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Use the substitution to find
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Find an expression for given that
Integrate
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Use integration by parts to find an expression for
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Find the exact value of
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Integrate
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Use the substitution to find the value of
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Use integration by parts to show that
where is a constant.
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Show that
can be written in the form
Hence find
writing your answer as a single logarithm.
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This topic pack contains questions on the following:
Integrate
Find an expression for given that
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Find the integral
Use calculus to evaluate
Find an expression for given that
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Integrate
Use calculus to find the value of
Find an expression for given that
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Use a suitable substitution to find
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Find an expression for given that
Find an expression for given that
Use calculus to find the exact value of
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Use calculus and the substitution to show that
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Given that
use calculus to find the exact value of
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Find
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Use the identity
to show that
Hence, or otherwise, find the integral
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Show that
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Use integration by parts to find, in terms of , the exact value of
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Show that
can be written in the form
Hence find
writing your answer as a single logarithm.
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Use calculus to find the value of
giving your answer to three significant figures.
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Given that the graph of passes through the point (0, 4) and that
Find
Explain why must be excluded from the domain of
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Show that
where is a constant.
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Use calculus to find
Write down
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Find the integral
Find an expression for given that
Use calculus to evaluate
giving your answer as a single logarithm.
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Integrate
Use calculus to find the value of
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Use a suitable substitution to find the following
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Use the substitution to show that
where is the constant of integration.
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Show that, for (where is an integer),
Use calculus and your result from part (a) to show that
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Use calculus to find the exact value of
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Find an expression for given that
Find an expression for given that
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Show that
Hence, or otherwise, find an expression for
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Write in the form where , and are all linear functions of .
Hence show that
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Use calculus to show that
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Use integration by parts to find
Show that
where is the constant of integration.
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Express
as partial fractions.
Hence, or otherwise, find
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Show that
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Given that and that show that
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Given
and that the graph of passes through the point (1, ln 144 ) find .
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Use calculus to find the value of
giving your answer in the form , where and are prime numbers to be found.
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Find an expression for given that
Integrate
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Find an expression for given that
Integrate
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Use calculus and the substitution to find the exact value of
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Find
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Show that
where is a constant, and is the constant of integration.
Use calculus to find the exact value of
writing your answer in the form , where and are rational numbers to be found.
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Show that
Hence, or otherwise, find the exact value of
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Show that
where and are constants, and
Using your working from part (a), or otherwise, evaluate
giving your answer in terms of and , where and are constants, and .
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Show that
Hence, or otherwise, find an expression for given that
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Find
Find
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Find the integral
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Use integration by parts to show that
where is the constant of integration.
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Show that there are no positive values of and that satisfy the equation
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Given that
and also that
find .
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Express in partial fractions.
Use your answer from part (a) to help find
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Given that and , show that
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