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ASMathsCambridge (CIE)Pure 2Exam QuestionsIntegrationFurther Integration

Further Integration (Cambridge (CIE) AS Maths: Pure 2): Exam Questions

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Use calculus to find

integral open parentheses x to the power of 2 space end exponent plus 5 minus 3 over x squared close parentheses d x

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1b
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Write down

integral 3 e to the power of 3 x end exponent d x

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2a
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Find the integral

integral 5 open parentheses e to the power of 5 x end exponent minus e to the power of negative 5 x end exponent close parentheses space d x

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Find an expression for y given that

y =integral open parentheses sin space x plus cos space x close parentheses space d x

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2c
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Use calculus to evaluate

integral subscript negative 8 end subscript superscript negative 2 end superscript 1 over x d x

giving your answer as a single logarithm.

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3a
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Integrate

integral 2 space sin x space cos x space d x

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Use calculus to find the value of

integral subscript 1 superscript 3 open parentheses 4 x plus 1 close parentheses to the power of 5 space end exponent d x

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4a
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Find an expression for f(x) given that

f(x) = integral fraction numerator 5 over denominator 2 x plus 3 end fraction d x

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Find an expression for y given that

fraction numerator d y over denominator d x end fraction equals 2 e to the power of 3 x minus 5 end exponent minus 5 e to the power of 5 x end exponent

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5a
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Show that

sin squared open parentheses 3 x plus 2 close parentheses space identical to 1 half open parentheses 1 minus cos open parentheses 6 x plus 4 close parentheses close parentheses

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Hence, or otherwise, find an expression for

integral sin squared open parentheses 3 x plus 2 close parentheses space d x

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