Class 12 Integrals worksheet

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   ∫ (−3x² + 4x + 2) dx equals:

   1. −x³ + 2x² + 2x + C
   2. −6x + 4 + C
   3. −3x³ + 4x² + 2x + C
   4. −x³ + 2x² − 2x + C

   Answer

   (a) −x³ + 2x² + 2x + C

   raise each power by one and divide by the new power

2. 2.

   ∫ sec²9x dx equals:

   1. 9 tan 9x + C
   2. (1/9) sec 9x tan 9x + C
   3. tan 9x + C
   4. (1/9) tan 9x + C

   Answer

   (d) (1/9) tan 9x + C

   a standard integral

3. 3.

   ∫₋₂¹ (3x + 1) dx equals:

   1. −3/2
   2. 5/2
   3. 13/2
   4. 3/2

   Answer

   (a) −3/2

   [(3/2)x² + x] from −2 to 1

Section B · short answer

1. 4.

   Find ∫ (9x⁵ + 5/x + 8eˣ) dx.

   Answer

   (3/2)x⁶ + 5 log|x| + 8eˣ + C

   ∫ xⁿ dx = xⁿ⁺¹/(n + 1), ∫ dx/x = log|x|, ∫ eˣ dx = eˣ

2. 5.

   Find ∫ x(x² + 4)² dx.

   Answer

   (1/6)(x² + 4)³ + C

   put t = x² + 4, dt = 2x dx

Section C · long answer

1. 6.

   Find ∫ dx/((x − 3)(x − 5)(x − 6)).

   Answer

   (1/6) log|x − 3| − (1/2) log|x − 5| + (1/3) log|x − 6| + C

   partial fractions: A = 1/6, B = −1/2, C = 1/3 (cover-up rule)

Fresh sheets for your child

In the app, every Integrals sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

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