Definite Integrals of Odd, Even and Periodic Function
Integral Calculus

86712 \(\int_{0}^{\pi} \sqrt{\frac{1+\cos 2 \mathrm{x}}{2}} \mathrm{dx}\) is equal to

1 0
2 2
3 1
4 -1
Integral Calculus

86713 \(\int_{0}^{1}|\sin 2 \pi x| d x\) is equal to

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

86714 \(\int_{0}^{\pi / 2} \frac{d \theta}{1+\tan \theta}\) is equal to

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

86715 What is the ratio of the two integrals \(\int_{0}^{\pi} f(\sin x) d x: \int_{0}^{\frac{\pi}{2}} f(\sin x) d x\) ?

1 \(1 / 2\)
2 2
3 \(\pi / 2\)
4 \(2 / \pi\)
Integral Calculus

86712 \(\int_{0}^{\pi} \sqrt{\frac{1+\cos 2 \mathrm{x}}{2}} \mathrm{dx}\) is equal to

1 0
2 2
3 1
4 -1
Integral Calculus

86713 \(\int_{0}^{1}|\sin 2 \pi x| d x\) is equal to

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

86714 \(\int_{0}^{\pi / 2} \frac{d \theta}{1+\tan \theta}\) is equal to

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

86715 What is the ratio of the two integrals \(\int_{0}^{\pi} f(\sin x) d x: \int_{0}^{\frac{\pi}{2}} f(\sin x) d x\) ?

1 \(1 / 2\)
2 2
3 \(\pi / 2\)
4 \(2 / \pi\)
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Integral Calculus

86712 \(\int_{0}^{\pi} \sqrt{\frac{1+\cos 2 \mathrm{x}}{2}} \mathrm{dx}\) is equal to

1 0
2 2
3 1
4 -1
Integral Calculus

86713 \(\int_{0}^{1}|\sin 2 \pi x| d x\) is equal to

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

86714 \(\int_{0}^{\pi / 2} \frac{d \theta}{1+\tan \theta}\) is equal to

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

86715 What is the ratio of the two integrals \(\int_{0}^{\pi} f(\sin x) d x: \int_{0}^{\frac{\pi}{2}} f(\sin x) d x\) ?

1 \(1 / 2\)
2 2
3 \(\pi / 2\)
4 \(2 / \pi\)
Integral Calculus

86712 \(\int_{0}^{\pi} \sqrt{\frac{1+\cos 2 \mathrm{x}}{2}} \mathrm{dx}\) is equal to

1 0
2 2
3 1
4 -1
Integral Calculus

86713 \(\int_{0}^{1}|\sin 2 \pi x| d x\) is equal to

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

86714 \(\int_{0}^{\pi / 2} \frac{d \theta}{1+\tan \theta}\) is equal to

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

86715 What is the ratio of the two integrals \(\int_{0}^{\pi} f(\sin x) d x: \int_{0}^{\frac{\pi}{2}} f(\sin x) d x\) ?

1 \(1 / 2\)
2 2
3 \(\pi / 2\)
4 \(2 / \pi\)