Definite Integrals — Important Questions
Telangana Open School (TOSS) · Class 12 · Mathematics
45 important questions from Definite Integrals for Telangana Open School (TOSS) Class 12 Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Definite Integrals
The value of \( \int_0^1 1 \, dx \) is:
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1
The integral of 1 from 0 to 1 is simply the length of the interval, which is 1.
Which property states that \( \int_a^b f(x) \, dx = \int_a^c f(x) \, dx + \int_c^b f(x) \, dx \)?
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Additivity of limits
This is the additivity property of definite integrals, allowing splitting the interval at any point c.
What is \( \int_0^\pi \sin x \, dx \)?
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2
The antiderivative of \( \sin x \) is \( -\cos x \). So, \( [-\cos x]_0^\pi = -\cos\pi + \cos0 = -(-1) + 1 = 2 \).
If \( f(x) \) is an odd function, then \( \int_{-a}^a f(x) \, dx \) equals:
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