Theorem of Definite Integrals and its Properties
Integral Calculus

86497 If \(\int_{1}^{k}\left(3 x^{2}+2 x+1\right) d x=11\), then \(k=\)

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

86498 \(\int_{0}^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^{4} x} d x=\)

1 \(\frac{\pi}{8}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86499 \(\int_{-5}^{5}\left[\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\right] d x=\)

1 \(3 \mathrm{e}^{5}\)
2 0
3 \(2 \mathrm{e}^{5}\)
4 1
Integral Calculus

86500 \(\int_{0}^{\pi / 4} \sin x \cdot \sec ^{2} x d x\)

1 \(2-\sqrt{2}\)
2 \(1-\sqrt{2}\)
3 \(\sqrt{2}-1\)
4 \(1+\sqrt{2}\)
Integral Calculus

86497 If \(\int_{1}^{k}\left(3 x^{2}+2 x+1\right) d x=11\), then \(k=\)

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

86498 \(\int_{0}^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^{4} x} d x=\)

1 \(\frac{\pi}{8}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86499 \(\int_{-5}^{5}\left[\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\right] d x=\)

1 \(3 \mathrm{e}^{5}\)
2 0
3 \(2 \mathrm{e}^{5}\)
4 1
Integral Calculus

86500 \(\int_{0}^{\pi / 4} \sin x \cdot \sec ^{2} x d x\)

1 \(2-\sqrt{2}\)
2 \(1-\sqrt{2}\)
3 \(\sqrt{2}-1\)
4 \(1+\sqrt{2}\)
Integral Calculus

86497 If \(\int_{1}^{k}\left(3 x^{2}+2 x+1\right) d x=11\), then \(k=\)

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

86498 \(\int_{0}^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^{4} x} d x=\)

1 \(\frac{\pi}{8}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86499 \(\int_{-5}^{5}\left[\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\right] d x=\)

1 \(3 \mathrm{e}^{5}\)
2 0
3 \(2 \mathrm{e}^{5}\)
4 1
Integral Calculus

86500 \(\int_{0}^{\pi / 4} \sin x \cdot \sec ^{2} x d x\)

1 \(2-\sqrt{2}\)
2 \(1-\sqrt{2}\)
3 \(\sqrt{2}-1\)
4 \(1+\sqrt{2}\)
Integral Calculus

86497 If \(\int_{1}^{k}\left(3 x^{2}+2 x+1\right) d x=11\), then \(k=\)

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

86498 \(\int_{0}^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^{4} x} d x=\)

1 \(\frac{\pi}{8}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86499 \(\int_{-5}^{5}\left[\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\right] d x=\)

1 \(3 \mathrm{e}^{5}\)
2 0
3 \(2 \mathrm{e}^{5}\)
4 1
Integral Calculus

86500 \(\int_{0}^{\pi / 4} \sin x \cdot \sec ^{2} x d x\)

1 \(2-\sqrt{2}\)
2 \(1-\sqrt{2}\)
3 \(\sqrt{2}-1\)
4 \(1+\sqrt{2}\)