Integral Calculus (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 6 - 9 of 17

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Question number: 6

» Integral Calculus » Evaluation of Simple Integrals

Appeared in Year: 2012

MCQ▾

Question

The value 20122012(sin(x3)+x5+1)dx is

Choices

Choice (4) Response
a.

4024

b.

0

c.

2012

d.

2013

Question number: 7

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2013

MCQ▾

Question

For x, t ∈ R let,

pt(x)=(sint)x2(2cost)x+sint

be a family of quadratic polynomials in x with variable coefficients. Let

A(t)=01pt(x)dx.

Which of the following statements are true?

(i) A(t)<0 for all t.

(ii) A(t) has infinitely many critical points.

(iii) A(t)=0 for infinitely many t

(iv) A(t)<0 for all t.

Choices

Choice (4) Response
a.

(i) and (ii) only

b.

(iii) and (iv) only

c.

(ii) and (iii) only

d.

(iv) and (i) only

Question number: 8

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2014

MCQ▾

Question

For a real number x let [x] denote the largest integer less than or equal to x . The smallest positive integer n for which the integer 1n[x][x]dx exceed 60 is –

Choices

Choice (4) Response
a.

9

b.

10

c.

8

d.

[6023]

Question number: 9

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2013

MCQ▾

Question

A function At(x) is defined as,

At(x)=(2sint)x2+(3cost)xcost,(Forx,tR)

It is a family of quadratic polynomials in x with variable coefficients. And also function,

B(t)=01At(x)dx Which of the following statements are true?

(i) A(t)<0,forallt

(ii) A(t) has infinitely many critical points.

(iii) A(t)>0,forallt (Model Paper)

Choices

Choice (4) Response
a.

(iii) and (i) only

b.

(i) and (ii) only

c.

(iii) only

d.

(ii) and (iii) only

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