Mathematics Practice Tests – Integration

Hello and Welcome to Mathematics Practice Tests - Integration

1. You are to attempt 5 random objectives questions ONLY.
2. Supply Your Full Name and Location in the text box below and begin immediately.
3. You can attempt as many times as possible
1.

Find the equation of the curve which passes through the point (2,5) and whose gradient at any point is given by 6x – 5.

A. 6x2 – 5x + 5
B. 6x2 + 5x + 5
C. 3x2 – 5x – 5
D. 3x2 – 5x + 3

2.

Find the area of the figure bounded by the given pair of curves y = x2 – x + 3 and y = 3

A. $\frac{17}{6}$ units (sq)      B. $\frac{7}{6}$ units (sq)     C. $\frac{5}{6}$ units (sq)     D. $\frac{1}{6}$ units (sq)

3.

Integrate x2 + 4x – 6 with respect to x. (NECO 2016)

A. x3 – 2x2 – 6x + C
B. x3 + 2x2 – 6x + C

C. $\dpi{110}&space;\frac{1}{3}$ x3 – 2x – 6

D. $\dpi{110}&space;\frac{1}{3}$ x3 + 2x2 – 6x + C

4.

If  $\dpi{110}&space;\frac{dy}{dx}$ = $\dpi{110}\frac{1}{2}\,&space;\left&space;(&space;Sin4x+Sin2x+1&space;\right&space;)$, find y

A. $\dpi{110}\frac{cos4x}{8}+\frac{cos2x}{4}+\frac{x}{2}+k$

B. -2 cos4x - cos2x + $\dpi{110}\frac{x}{2}$

C. $\dpi{110}-\frac{cos4x}{8}-\frac{cos2x}{4}+\frac{x}{2}&space;+k$

D. 2 cos4x + cos2x + $\dpi{110}\frac{x}{2}$

5.

Find the value of $\int_{0}^{\pi&space;}\frac{cos^{2}\theta&space;-1}{sin^{2}\theta&space;}d\theta$

A. π     B. $\frac{\pi&space;}{2}$     C. $\frac{-\pi&space;}{2}$     D. - π

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