Integral Calculus (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 10 - 13 of 17

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Question number: 10

» 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 and {x}=x[x] . Let n be a positive integer. Then 0ncos(2π[x]{x})dx is equal to –

Choices

Choice (4) Response

a.

0

b.

2n1

c.

1

d.

n

Question number: 11

» Integral Calculus » Fundamental Integrals Involving Functions

Appeared in Year: 2014

MCQ▾

Question

A continuous function f:RR satisfies the equation,

f(x)=x+0xf(t)dt.

Which of the following options is true?

Choices

Choice (4) Response

a.

f(x+y)=f(x)f(y)

b.

f(x+y)=f(x)+f(y)+f(x)f(y)

c.

f(x+y)=f(x)+f(y)

d.

f(x+y)=f(xy)

Question number: 12

» Integral Calculus » Evaluation of Definite Integrals

Appeared in Year: 2014

MCQ▾

Question

Let, In=0π2xncosxdx Where, n is a non-negative integer. Then,

n=2(Inn!+In2(n2)!)=_.

Choices

Choice (4) Response

a.

eπ21π2

b.

eπ2

c.

eπ21

d.

eπ2π2

Question number: 13

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2013

MCQ▾

Question

Let n be a positive integer. For a real number x , let [x] denoted the largest integer not exceeding x and {x}=x[x] . Then,

1n+1({x})[x][x]dx is equal to – (Model Paper)

Choices

Choice (4) Response

a.

loge(n)

b.

1n+1

c.

nn+1

d.

1+12++1n

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