JAMB Mathematics Past Questions & Answers - Page 356

1,777.

Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\)

A.

zero

B.

1

C.

2

D.

3

Correct answer is C

\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\\
=sin\frac{\pi}{2} - sin\frac{-\pi}{2}\)
= sin90 – sin-90
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2

1,778.

Evaluate \(\int_1 ^2(6x^2-2x)dx\)

A.

16

B.

13

C.

12

D.

11

Correct answer is D

\(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\\
= [2x^3 - x^2]_1^2\)
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11

1,779.

Find the minimum value of the function y = x(1+x)

A.

-1/4

B.

-1/2

C.

1/4

D.

1/2

Correct answer is A

y = x(1+x)
= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4

1,780.

Differentiate sin x - x cos x

A.

x cos x

B.

x sin x

C.

-x cos x

D.

-x sin x

Correct answer is B

sin x - x cos x
dy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x