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PUNE MCA Exam 2015 Question Paper with answers for online practice

Question : 1 of 59

Marks: +1, -0

\int\limits_{0}^{a}

\int\limits_{0}^{na}

Solution:

Concept:

The function is periodic with period

a

, so the integral over each interval of length

a

is the same.

Explanation:

Given

f(x) = f(x + a)

, the function repeats every

a

units.

The integral over one period is

\int_0^a f(x) \, dx = k

The interval

[0, na]

contains exactly

n

complete periods of length

a

Therefore,

\int_0^{na} f(x) \, dx = n \cdot \int_0^a f(x) \, dx = nk

Answer:

\int_0^{na} f(x) \, dx = nk

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