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If f(2a − x) = −f(x), prove that
\[\int\limits_0^{2a} f\left( x \right) dx = 0 .\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If f is an integrable function, show that
\[\int\limits_{- a}^a f\left( x^2 \right) dx = 2 \int\limits_0^a f\left( x^2 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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If f is an integrable function, show that
\[\int\limits_{- a}^a x f\left( x^2 \right) dx = 0\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If f (x) is a continuous function defined on [0, 2a]. Then, prove that
\[\int\limits_0^{2a} f\left( x \right) dx = \int\limits_0^a \left\{ f\left( x \right) + f\left( 2a - x \right) \right\} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If f(x) is a continuous function defined on [−a, a], then prove that
\[\int\limits_{- a}^a f\left( x \right) dx = \int\limits_0^a \left\{ f\left( x \right) + f\left( - x \right) \right\} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\int_0^\pi xf\left( \sin x \right)dx = \frac{\pi}{2} \int_0^\pi f\left( \sin x \right)dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^3 \left( x + 4 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^2 \left( x + 3 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_1^3 \left( 3x - 2 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_{- 1}^1 \left( x + 3 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^5 \left( x + 1 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_1^3 \left( 2x + 3 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_3^5 \left( 2 - x \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^2 \left( x^2 + 1 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_2^3 \left( 2 x^2 + 1 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_1^2 \left( x^2 - 1 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^2 \left( x^2 + 4 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_1^4 \left( x^2 - x \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^1 \left( 3 x^2 + 5x \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
