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Rate of change of area of circle with respect to radius r:

2πr
πr²
π
πr

Calculus (Basic)

∫(e^(3x)) dx = ?

e^(3x)/3 + C
3 e^(3x)
e^x + C
3x e^(3x)

Calculus (Basic)

∫(sin 2x) dx = ?

-cos 2x/2 + C
cos 2x/2 + C
sin 2x + C
-sin 2x + C

Calculus (Basic)

∫(x³ – 2x + 5) dx = ?

x⁴/4 – x² + 5x + C
x³ – x² + 5x
x⁴/4 – 2x² + 5x
x³/3 – x² + 5x

Calculus (Basic)

Minima of f(x) = x² – 4x + 3:

x = 2
x = 1
x = 3
x = 4

Calculus (Basic)

Maxima of f(x) = x² – 6x + 8:

x = 3
x = 2
x = 1
x = 4

Calculus (Basic)

If y = x³ – 3x² + 5, find d²y/dx²:

6x – 6
3x² – 6
2x – 3
6x + 6

Calculus (Basic)

∫cosec² x dx = ?

-cot x + C
cot x + C
-tan x + C
tan x + C

Calculus (Basic)

∫sec² x dx = ?

tan x + C
sec x + C
cos x + C
sin x + C

Calculus (Basic)

∫(2x)/(x² + 1) dx = ?

ln(x² + 1) + C
2 ln(x)
x² + C
1/(x² +1)

Calculus (Basic)

If y = x² e^x, dy/dx = ?

2x e^x + x² e^x
x² e^x
2x e^x
e^x

Calculus (Basic)

∫(1/x²) dx = ?

-1/x + C
1/x + C
x²/2 + C
ln x

Calculus (Basic)

∫(3x² – 2x + 1) dx = ?

x³ – x² + x + C
x³ – 2x² + x
3x³/3 – 2x² + x
x³ – x² + 1

Calculus (Basic)

Minima of f(x) = x² + 4x + 3 occurs at x = ?

-2
2
-1
1

Calculus (Basic)

Maxima of f(x) = -x² + 4x – 1 occurs at x = ?

2
1
3
4

Calculus (Basic)

For f(x) = x⁴ – 4x³, stationary points are at x = ?

0, 3
1, 2
2, 3
0, 2

Calculus (Basic)

If f(x) = x² + 2x, d²f/dx² = ?

2
2x
1
4x

Calculus (Basic)

Rate of change of y = 5x² at x = 3:

30
25
15
20

Calculus (Basic)

If f(x) = 2x³ – 3x² + x – 5, f'(x) = ?

6x² – 6x + 1
6x² – 3x + 1
3x² – 3x + 1
6x² – 3x – 5

Calculus (Basic)

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