Integration quiz: N(A)-Level Additional Mathematics (SEAB 4051) quiz

differentiation

addition

factorising

substitution

$\dfrac{x^4}{4} + c$

$3x^2 + c$

$x^4 + c$

$\dfrac{x^2}{2} + c$

to make the answer larger

to represent the constant lost when differentiating

because limits are missing the variable

it is optional and can be dropped

$2x^3 - 2 + c$

$12x - 2 + c$

$2x^3 - 2x + c$

$6x^3 - 2x + c$

$5x + c$

$5 + c$

$0 + c$

$\dfrac{5x^2}{2} + c$

$F(a) - F(b)$

$F(b) - F(a)$

$F(a) + F(b)$

$F(b) \times F(a)$

constants are never used in calculus

the limits replace the function

the integral is always zero

the constant cancels when subtracting the limits

$8$

$12$

$4$

$6$

$9$

$8$

$4$

$6$

$f(b) - f(a)$

$\displaystyle\int_a^b f(x)\,dx$

the gradient at $b$

$\dfrac{f(a) + f(b)}{2}$

$8$ square units

$4$ square units

$\dfrac{8}{3}$ square units

$2$ square units

positive

the same as the area, sign and all

always zero

negative, so you take its magnitude for area

$\dfrac{x^3}{3} + \dfrac{3x^2}{2} + c$

$2x + 3 + c$

$x^3 + 3x^2 + c$

$\dfrac{x^3}{3} + 3x + c$

$4 + c$

$2x^2 + c$

$4x^2 + c$

$x^2 + c$