8.2.1 Integrating x^n and related sums Quiz: Pearson Edexcel Maths, Unit 8

The 20 questions

1. What is the result of integrating x to the power of n with respect to x, for n not equal to -1?

   • nx^(n+1) + c
   • nx^(n-1) + c
   • x^(n+1)/(n+1) + c
   • x^n/(n+1) + c

2. What represents the constant of integration in indefinite integrals?

   • + c
   • + 0
   • + x
   • + k

3. What is the integral of 4x^3 with respect to x?

   • 12x^2 + c
   • x^3 + c
   • 4x^4 + c
   • x^4 + c

4. What is the integral of 5 with respect to x?

   • 5 + c
   • 5x + c
   • 0 + c
   • 5x^2 + c

5. What value of n makes the standard rule for integrating x^n invalid?

   • 1
   • 2
   • 0
   • -1

6. What is the integral of x^(-2) with respect to x?

   • -2x^(-3) + c
   • ln|x| + c
   • -x^(-1) + c
   • x^(-1)/(-1)

7. Rewrite 1 over x^3 in index form for integration.

   • x^3
   • 3x^(-1)
   • x^(-3)
   • -3x

8. Rewrite the square root of x in index form before integrating.

   • x^(-1/2)
   • x^2
   • x^(1/2)
   • 2x

9. What is the integral of 3x^2 + 2x with respect to x?

   • x^3 + 2x^2 + c
   • 3x^3 + 2x^2 + c
   • x^3 + x^2 + c
   • 6x + 2 + c

10. Find the integral of (x^2 + 1) over x^2 with respect to x.

    • x^3/3 + x + c
    • 1 + x^(-2) + c
    • x + x^(-2) + c
    • x - x^(-1) + c

11. What is the integral of 2 times the square root of x with respect to x?

    • (4/3)x^(3/2) + c
    • 4x^(1/2) + c
    • (1/3)x^(3/2) + c
    • x^(3/2) + c

12. What process is the reverse of differentiation?

    • Factorisation
    • Expansion
    • Substitution
    • Integration

13. What term describes integration without upper and lower limits?

    • Indefinite integral
    • Exact integral
    • Particular integral
    • Definite integral

14. What is the integral of (4 / x^2) with respect to x?

    • -4x^(-1) + c
    • -8x^(-1) + c
    • 8x^(-3) + c
    • 4ln|x| + c

15. What is the integral of x(x + 2) after expanding?

    • x^3 + 2x^2 + c
    • x^2 + 2x + c
    • (1/3)x^3 + x^2 + c
    • (1/2)x^3 + x^2 + c

16. Find the integral of 5x^4 - 3x^2 with respect to x.

    • x^5 - x^3 + c
    • 5x^5 - 3x^3 + c
    • 20x^3 - 6x + c
    • x^5 - 3x^3 + c

17. What is the integral of (1 / 2x^3) with respect to x?

    • -(3/2)x^(-4) + c
    • (1/2)ln|x| + c
    • -2x^(-2) + c
    • -(1/4)x^(-2) + c

18. What is the result of term-by-term integration of a sum of functions?

    • Sum of integrals
    • Product of integrals
    • Derivative of sum
    • Quotient of integrals

19. What happens to a constant factor k inside an integral term during integration?

    • It remains
    • It becomes zero
    • It squares
    • It becomes one

20. What is the integral of 6x^5 minus 2x with respect to x?

    • x^6 - x^2
    • 6x^6 - 2x^2 + c
    • 30x^4 - 2 + c
    • x^6 - x^2 + c

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