Integral Calculus (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 1 - 5 of 17

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Question number: 1

» Integral Calculus » Evaluation of Definite Integrals

Appeared in Year: 2010

MCQ▾

Question

Let In=01(logx)ndx , where n is non-negative integer. Then I2011+2011I2010 is equal to –

Choices

Choice (4) Response

a.

I100+100I99

b.

I1000+999I998

c.

I890+890I889

d.

I53+54I52

Question number: 2

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2012

MCQ▾

Question

The value of the integral ππcos2x1+axdx , where a>0, is –

Choices

Choice (4) Response

a.

π2

b.

ax

c.

π

d.

2π

Question number: 3

» Integral Calculus » Evaluation of Simple Integrals

Appeared in Year: 2012

MCQ▾

Question

Let [x] and {x} are be the integer part and fractional part of a real number x respectively. The value of the integral, 05[x]{x}dx is –

Choices

Choice (4) Response

a.

5

b.

52

c.

35.5

d.

34.5

Question number: 4

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2012

MCQ▾

Question

The value 0π2(sinx)2+1dx0π2(sinx)21dx is –

Choices

Choice (4) Response

a.

212+1

b.

2+12

c.

22

d.

2+121

Question number: 5

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2012

MCQ▾

Question

Consider,

L=20123+20133++30113

R=20133+20143++30123

andI=20123012x3dxThen

Choices

Choice (4) Response

a.

L+R<2I

b.

L+R>2I

c.

L+R=2I

d.

LR=I

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