Definite Integral as Limit of a Sum
Integral Calculus

86405 \(\int_{-\pi}^{\pi} \sin x[f(\cos x)] d x=\)

1 \(2 \mathrm{f}(\pi)\)
2 \(2 \mathrm{f}(2)\)
3 \(2 \mathrm{f}(1)\)
4 None of these
Integral Calculus

86415 \(\int_{0}^{\pi} \frac{x}{\sin x}\left(3 \cos ^{2} x+2 \sin x+\sin ^{3} x-3\right) d x=\)

1 \(\frac{\pi(5 \pi-12)}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{2}(5 \pi-6)\)
4 \(\frac{\pi(5 \pi-12)}{6}\)
Integral Calculus

86416 \(\int_{-1}^{1} \frac{|x|}{x} d x=\)

1 1
2 -1
3 0
4 \(\frac{1}{2}\)
Integral Calculus

86417 \(\int_{2}^{5} \sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}} d x=\)

1 \(16 / 3\)
2 \(32 / 3\)
3 \(28 / 3\)
4 \(4 / 3\)
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Integral Calculus

86405 \(\int_{-\pi}^{\pi} \sin x[f(\cos x)] d x=\)

1 \(2 \mathrm{f}(\pi)\)
2 \(2 \mathrm{f}(2)\)
3 \(2 \mathrm{f}(1)\)
4 None of these
Integral Calculus

86415 \(\int_{0}^{\pi} \frac{x}{\sin x}\left(3 \cos ^{2} x+2 \sin x+\sin ^{3} x-3\right) d x=\)

1 \(\frac{\pi(5 \pi-12)}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{2}(5 \pi-6)\)
4 \(\frac{\pi(5 \pi-12)}{6}\)
Integral Calculus

86416 \(\int_{-1}^{1} \frac{|x|}{x} d x=\)

1 1
2 -1
3 0
4 \(\frac{1}{2}\)
Integral Calculus

86417 \(\int_{2}^{5} \sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}} d x=\)

1 \(16 / 3\)
2 \(32 / 3\)
3 \(28 / 3\)
4 \(4 / 3\)
Integral Calculus

86405 \(\int_{-\pi}^{\pi} \sin x[f(\cos x)] d x=\)

1 \(2 \mathrm{f}(\pi)\)
2 \(2 \mathrm{f}(2)\)
3 \(2 \mathrm{f}(1)\)
4 None of these
Integral Calculus

86415 \(\int_{0}^{\pi} \frac{x}{\sin x}\left(3 \cos ^{2} x+2 \sin x+\sin ^{3} x-3\right) d x=\)

1 \(\frac{\pi(5 \pi-12)}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{2}(5 \pi-6)\)
4 \(\frac{\pi(5 \pi-12)}{6}\)
Integral Calculus

86416 \(\int_{-1}^{1} \frac{|x|}{x} d x=\)

1 1
2 -1
3 0
4 \(\frac{1}{2}\)
Integral Calculus

86417 \(\int_{2}^{5} \sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}} d x=\)

1 \(16 / 3\)
2 \(32 / 3\)
3 \(28 / 3\)
4 \(4 / 3\)
Integral Calculus

86405 \(\int_{-\pi}^{\pi} \sin x[f(\cos x)] d x=\)

1 \(2 \mathrm{f}(\pi)\)
2 \(2 \mathrm{f}(2)\)
3 \(2 \mathrm{f}(1)\)
4 None of these
Integral Calculus

86415 \(\int_{0}^{\pi} \frac{x}{\sin x}\left(3 \cos ^{2} x+2 \sin x+\sin ^{3} x-3\right) d x=\)

1 \(\frac{\pi(5 \pi-12)}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{2}(5 \pi-6)\)
4 \(\frac{\pi(5 \pi-12)}{6}\)
Integral Calculus

86416 \(\int_{-1}^{1} \frac{|x|}{x} d x=\)

1 1
2 -1
3 0
4 \(\frac{1}{2}\)
Integral Calculus

86417 \(\int_{2}^{5} \sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}} d x=\)

1 \(16 / 3\)
2 \(32 / 3\)
3 \(28 / 3\)
4 \(4 / 3\)