Mathematics ECAT Pre Engineering Chapter 19 Integration Online Test With Answers

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Mathematics ECAT Pre Engineering Chapter 19 Integration Online Test

Sr. # Questions Answers Choice
1 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
2 An equation in which at least one term contains dy/dx, d2 y /dx2etc, is called. Differential equation Initial condition General solution Singular equation
3 The general solution of the differential equation x dy / dx = 1 + y is: 2 1 3 None
4 The area enclosed between the graph y = x2 -4x and the x- axis is: 20/3 41/3 32/3 25/3
5 The area under the curve y = 1/x2 between x = 1 and x =4 is: -25 0.75 -0.35 -10
6 The area between the x-axis the curve y =4x-x2 is : 32/2 15 18 21
7 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
8 ∫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 |
9 ∫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
10 ∫ 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
11 ∫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)
12 ∫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)
13 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
14 ∫f(x) is known as: Definite itegral Indefinite integral Fixed integral Multiple integral
15 An integral of 1/x dx is: 1/x<sup>2</sup> 1/-x<sup>2</sup> 1/lnx lnx
16 Which of the following integrals can be evaluated
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18 <span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π</i></span> <span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π/6</i></span> -<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π/2</i></span> 2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π</i></span>
19 0 1 2 4
20 Always negative Zero Always positive Infinity
21 If the graph of f is entirely below the x-axis, then the value of definite integral is = 0 &lt; 0 &gt; 0 None
22 If the lower limit of an integral is a constant and the upper limit is a variable, then the integral is a Constant function Variable value Function of upper limit All
23 The arbitrary constants involving in the solution can be determined by the given conditions. Such conditions are called Boundaries Variable separable Initial values None
24 Y = -x log x -x + c Y = x log x + x Y = x log x - x + c None of these
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27 X = 100 sin<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);"><i>θ</i></span> X = 10 sin<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>θ</i></span> X = 100 sec<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>θ</i></span> None of these
28 A variable A constant 0 None of these
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