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Mathematics
Evaluate the following integral:
\[\int_{- \pi}^\pi \frac{2x\left( 1 + \sin x \right)}{1 + \cos^2 x}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate the following integral:
\[\int_{- 2}^2 \frac{3 x^3 + 2\left| x \right| + 1}{x^2 + \left| x \right| + 1}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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Evaluate the following integral:
\[\int_{- \frac{3\pi}{2}}^{- \frac{\pi}{2}} \left\{ \sin^2 \left( 3\pi + x \right) + \left( \pi + x \right)^3 \right\}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate the following integral:
\[\int_0^\pi \left( \frac{x}{1 + \sin^2 x} + \cos^7 x \right)dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate the following integral:
\[\int_0^{2\pi} \sin^{100} x \cos^{101} xdx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate the following integral:
\[\int_0^\frac{\pi}{2} \frac{a\sin x + b\sin x}{\sin x + \cos x}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate :
\[\int\limits_0^{3/2} \left| x \sin \pi x \right|dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^k \frac{1}{2 + 8 x^2} dx = \frac{\pi}{16},\] find the value of k.
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int_\pi^\frac{3\pi}{2} \sqrt{1 - \cos2x}dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
\[\int_a^b xf\left( x \right)dx = \left( \frac{a + b}{2} \right) \int_a^b f\left( x \right)dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
