ECAT Mathematics Chapter 19 Integration Online Test With Answers

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ECAT Mathematics Chapter 19 Integration Online Test

Sr. # Questions Answers Choice
1 2x + 3 x<sup>2</sup>+ 3 + c
2
3 none of these
4 The process of finding a function whose derivative is given is called a Differentiation Integration Differential None
5 The set of all antiderivaties of f(= ∫f(x)dx) is the Definite integral Indefinite integral Integral Area
6 The function ø(x) is ananti derivativeof function f (x),x∈Df if ø′(x) =∫f(x)dx ø(x) =∫f(x)dx ø′(x) =f(x) ø(x) =∫′(x)dx
7 The number of arbitrary constants in the general solution of a differential equation is equal to the different equation Order Degree Variables All are correct
8 The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is 1.2% 1.5% 0.16% 100.16%
9 ∛8.6 is approximately equal to 2.488 2.48 2.0488 2.05
10 The approximate increase in the area of a circular disc if its diameter increased form 44cm to 44.4cm is 0.4cm 8.8πcm 17.6 πcm 35.2πcm
11 f(x)g(x)- ∫g(x) f′(x) dx is equal to ∫f(x)g′(x)dx ∫f′(x)g(x)dx ∫f′(x)g(x)′dx ∫f(x)g(x)dx
12 The area bounded by y = x (x2 - 4) and below x - axis is 4 0 -4 8
13 Archimedes approximate the function by horizontal function and the area under f by the sum of small Parallelograms Squares Retangles Polygons
14 The solution of differential equation: dy/dx+y/x = x<sup>2 </sup>is : 4xy = x<sup>4</sup>+ c 4x = x<sup>4</sup>= c 4 y = x<sup>4</sup>+ c 4x=4x<sup>3</sup> + c
15 An equation in which at least one term contains dy/dx, d2 y /dx2etc, is called. Differential equation Initial condition General solution Singular equation
16 The general solution of the differential equation x dy / dx = 1 + y is: 2 1 3 None
17 The area enclosed between the graph y = x2 -4x and the x- axis is: 20/3 41/3 32/3 25/3
18 The area under the curve y = 1/x2 between x = 1 and x =4 is: -25 0.75 -0.35 -10
19 The area between the x-axis the curve y =4x-x2 is : 32/2 15 18 21
20 The area between the x-axis and the curve y = x2 + 1 from x = 1 to 2 is: 15/6 15/4 10/4 10/3
21 ∫x/Sin2 x dx is equal to: x cot x + ln|sin⁡x | -x cot x - ln|sin⁡x | x cot x - ln|sin⁡x | x. tan x- ln|sec⁡x |
22 ∫x sin xdx is equal to: sin x/x + cos x sin x - cos x/x x cos x + sin x - x cos x + sin x
23 ∫ x cos dx is equal to : x cos x + sin x cos x + x sin x x cos x + x sin x x sin x + cos x
24 ∫sin(ax+b) dx is equal to: 1/2a cos (ax + b) -1/a cos (ax +b) 1/a cos (ax +b) 1/a ln (ax + b)
25 ∫Sec2 (ax + b) dx is equal to: tan<sup>2</sup> (ax + b) 1/a tan<sup>2</sup> (ax + b) 1/atan (ax +b) tan (ax + b)
26 The integral of 3x5dx is: 15 x<sup>4</sup> x<sup>6 </sup>/2 1/6x<sup>5</sup> x<sup>5 </sup>/ln3
27 ∫f(x) is known as: Definite itegral Indefinite integral Fixed integral Multiple integral
28 An integral of 1/x dx is: 1/x<sup>2</sup> 1/-x<sup>2</sup> 1/lnx lnx
29 Which of the following integrals can be evaluated
30
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