$\int_{-1}^{1} x^{17} \cos^{4} x \, dx = $
- A$ -2 $
- B$ -1 $
- C$ 0 $
- D$ 2 $
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Similar Questions
$\int_0^{2 \pi} \sin ^3 x \cos ^2 x \, dx = $ . . . . . . .
The integral value $\int_{-2}^{0} [x^3 + 3x^2 + 3x + 3 + (x + 1)\cos(x + 1)] \, dx$ is
MediumIIT 2005
View SolutionMatch the following:
List-$I$ List-$II$ $I. \int_{-1}^1 x|x| dx$ $(a) \frac{\pi}{2}$ $II. \int_0^{\pi/2} \left(1 + \log \left(\frac{4+3\sin x}{4+3\cos x}\right)\right) dx$ $(b) \int_0^a 2f(x) dx$ $III. \int_0^a f(x) dx$ $(c) \int_0^a [f(x) + f(-x)] dx$ $IV. \int_{-a}^a f(x) dx$ $(d) 0$ $(e) \int_0^a f(a-x) dx$
| List-$I$ | List-$II$ |
|---|---|
| $I. \int_{-1}^1 x|x| dx$ | $(a) \frac{\pi}{2}$ |
| $II. \int_0^{\pi/2} \left(1 + \log \left(\frac{4+3\sin x}{4+3\cos x}\right)\right) dx$ | $(b) \int_0^a 2f(x) dx$ |
| $III. \int_0^a f(x) dx$ | $(c) \int_0^a [f(x) + f(-x)] dx$ |
| $IV. \int_{-a}^a f(x) dx$ | $(d) 0$ |
| $(e) \int_0^a f(a-x) dx$ |
$\int_{-\pi}^{\pi} |\pi - |x|| \, dx$ is equal to :
The true set of values of $a$ for which the inequality $\int_{a}^{0} (3^{-2x} - 2 \cdot 3^{-x}) \, dx \geq 0$ is true is:
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