Recall · M4U-P1-QP-INTEGRATION-POWER-INTEGRALS-01
reverse power rule
Maths4U Original · Short practice
An antiderivative of \(6x^2\) is \(ax^3+C\). Find \(a\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Pure 1 course · All short practice · Notes & examples
Maths4U Original · 9709 Pure 1
Power integrals, constants and limits
Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.
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Method · M4U-P1-QP-INTEGRATION-POWER-INTEGRALS-02
linear inner factor
Maths4U Original · Short practice
An antiderivative of \((2x+1)^3\) is \(a(2x+1)^4+C\). Find \(a\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Apply · M4U-P1-QP-INTEGRATION-POWER-INTEGRALS-03
improper endpoint
Maths4U Original · Short practice
Find the improper integral \(\int_0^1 x^{-1/2}\,dx\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Check understanding · M4U-P1-QP-INTEGRATION-POWER-INTEGRALS-04
power exception
Maths4U Original · Short practice
For which power does \(\int x^n\,dx=x^{n+1}/(n+1)+C\) fail?Choose one answer.
Syllabus follow-up · M4U-P1-QP-INTEGRATION-POWER-INTEGRALS-05
negative power with linear inner function
Maths4U Original · Short practice
For \(x>-1/3\), an antiderivative of \((3x+1)^{-2}\) is \(a(3x+1)^{-1}+C\). Find \(a\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-POWER-INTEGRALS-01
reverse power rule
Maths4U Original · Short practice
An antiderivative of \(9x^2\) is \(ax^3+C\). Find a.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-POWER-INTEGRALS-02
linear inner factor
Maths4U Original · Short practice
An antiderivative of \((3x+2)^3\) is \(a(3x+2)^4+C\). Find a.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-POWER-INTEGRALS-03
improper endpoint
Maths4U Original · Short practice
Evaluate the improper integral \(\int_0^1x^{-2/3}\,dx\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-POWER-INTEGRALS-04
power exception
Maths4U Original · Short practice
For which exponent n is the ordinary power-integral formula for \((7x-1)^n\) invalid because n+1=0?Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-POWER-INTEGRALS-05
negative power with linear inner function
Maths4U Original · Short practice
For x greater than -2/5, an antiderivative of \((5x+2)^{-2}\) is \(a(5x+2)^{-1}+C\). Find a.Enter one number or fraction. Round decimals to at least six decimal places when needed.