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Integral Calculus | Mathematics - Exercise 11.13: Choose the correct answer | 11th Mathematics : Chapter 11 : Integral Calculus

Chapter: 11th Mathematics : Chapter 11 : Integral Calculus

Exercise 11.13: Choose the correct answer

Multiple choice questions with answers / choose the correct answer with answers - Maths Book back 1 mark questions and answers with solution for Exercise Problems - Mathematics : Integral Calculus

Integral Calculus (Mathematics)


Choose the correct or the most suitable answer from given four alternatives.

 

(1) If ∫ f (x)dx = g(x) + c, then ∫ f (x)g′(x)dx 

(1) ∫(f (x))2 dx 

(2) ∫ f (x)g(x)dx 

(3) ∫ f ′(x)g(x)dx

(4) ∫(g(x))2 dx

Ans: (1)


Solution


 

(2) If , then the value of k is 

(1) log 3 

(2) − log 3

(3) – 1 / log 3

(4) 1 / log 3

Ans: (3)


Solution


 

(3) If  ∫ f ′(x)ex2dx = (x − 1)ex2 + c , then f(x) is 

(1) 2x3x2/2 + x + c 

(2) x3/2 + 3x2 + 4x + c 

(3) x3 + 4x2 + 6x + c 

(4) 2x3/3 - x2+ x+ c

Ans: (4)


Solution


 

(4) The gradient (slope) of a curve at any point (x, y) is [x2 – 4]/ x2 . If the curve passes through the point (2, 7), then the equation of the curve is

(1) y = x + 4/x + 3 

(2) y = x + 4/x + 4 

(3) y = x2 + 3x + 4 

(4) y = x2 − 3x + 6

Ans: (1)


Solution


 

(5)  is 

(1) cot(xex ) + c 

(2) sec(xex ) + c 

(3) tan(xex ) + c 

(4) cos( xex ) + c

Ans: (3)


Solution


 

(6)  is 

(1) √tan x + c 

(2) 2√tan x + c 

(3) ½ √tan x + c 

(4) ¼ √tan x + c

Ans: (1)


Solution


 

(7) ∫sin3xdx is


Ans: (3)


Solution


 

(8)  is 

(1) x + c 

(2) [ x3/3] + c 

(3) [3/ x3] + c 

(4) [1/ x2] + c

Ans: (2)


Solution


 

(9)  is

 (1) tan−1 (sin x ) + c 

(2) 2sin−1 (tan x ) + c 

(3) tan−1 (cos x ) + c 

(4) sin−1 (tan x ) + c

Ans: (4)


Solution


 

(10)   is 

(1) x2 + c 

(2) 2x2 + c 

(3) x2/2 + c 

(4) − x2/2  + c

Ans: (3)


Solution


 

(11) ∫ 23 x+5 dx is 


Ans: (4)


Solution


 

(12)  is 


Ans: (2)


Solution


 

(13)  is 

(1) ex tan−1 (x + 1) + c 

(2) tan−1 (ex ) + c 

(3) ex [(tan−1 x)2/2] + c 

(4) ex tan−1x + c

Ans: (4)


Solution


 

(14)  is 

(1) cot x + sin−1 x + c 

(2) − cot x + tan−1 x + c 

(3) − tan x + cot−1 x + c 

(4) − cot x − tan−1 x + c 

Ans: (4)


Solution


 

(15) ∫ x2 cos x dx is 

(1) x2 sin x + 2x cos x − 2sin x + c 

(2) x2 sin x − 2x cos x − 2sin x + c 

(3) − x2 sin x + 2x cos x + 2sin x + c 

(4) − x2 sin x − 2x cos x + 2sin x + c 

Ans: (1)


Solution


 

(16)  is 

(1) √[1-x2] + sin−1 x + c 

(2) sin−1 x −√[1-x2] + c

(3) log | x + √[1-x2] | − √[1-x2] + c 

(4) √[1-x2] + log | x + √[1-x2] | +c

Ans: (2)


Solution


 

 (17)  is 

(1) log | ex |- log | ex - 1| + c 

(2) log | ex | + log | ex - 1| + c 

(3) log | ex - 1| -  log | ex | + c 

(4) log | ex + 1| - log | ex | + c 

Ans: (3)


Solution


 

(18) ∫e−4x cos x dx is


Ans: (2)


Solution


 

(19) 


Ans: (4)


Solution


 

(20) ∫e -7x sin 5x dx is 

(1) e−7x/74 [−7sin 5x − 5cos5x ] + c

(2) e−7x/74 [7sin 5x + 5cos5x ] + c

(3) e−7x /74 [7sin 5x − 5cos5x ] + c

(4) e−7x /74 [-7sin 5x + 5cos5x ] + c

Ans: (1)


Solution


 

(21) ∫x2ex/2dx is

(1) x2ex/2 – 4xex/2 – 8ex/2 + c

(2) 2x2ex/2 – 8xex/2 – 16ex/2 + c

(3) 2x2ex/2 – 8xex/2 + 16ex/2 + c

(4) [x2ex/2 / 2] – [xex/2 /4] +[ex/2 /8 ]+ c

Ans: (3)


Solution


 

(22) 


Ans: (4)


Solution


 

(23) 


Ans: (3)


Solution


 

(24) ∫sin √xdx is 

(1) 2(− √x cos√x + sin √x) + c 

(2) 2(− √x cos√x - sin √x) + c 

(3) 2(− √x sin√x - cos √x) + c 

(4) 2(− √x sin√x + cos √x) + c 

Ans: (1)


Solution


 

(25) ∫e√x dx is

(1) 2 √x (1− ex) + c 

(2) 2 √x (ex − 1) + c

(3) 2ex (1− √x ) + c 

(4) 2ex (√x − 1) + c

Ans: (4)


Solution



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11th Mathematics : Chapter 11 : Integral Calculus


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