Definite Integral as Limit of a Sum
Integral Calculus

86399 \(\int_{0}^{3}\left|x^{2}-3 x+2\right| d x=\)

1 \(\frac{3}{2}\)
2 \(\frac{1}{6}\)
3 \(\frac{11}{6}\)
4 \(\frac{11}{2}\)
Integral Calculus

86400 If \(\int_{0}^{a} \frac{d x}{4+x^{2}}=\frac{\pi}{8}\), then the value of \(a=\)

1 1
2 2
3 3
4 4
Integral Calculus

86402 The value of \(x\) that satisfies the equation \(\int_{\sqrt{2}}^{x} \frac{d t}{|t| \sqrt{t^{2}-1}}=\frac{\pi}{12}\) is

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

86403 \(\int_{1}^{e^{2}} \frac{\mathbf{d x}}{\mathbf{x}(1+\log x)^{2}}=\)

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

86399 \(\int_{0}^{3}\left|x^{2}-3 x+2\right| d x=\)

1 \(\frac{3}{2}\)
2 \(\frac{1}{6}\)
3 \(\frac{11}{6}\)
4 \(\frac{11}{2}\)
Integral Calculus

86400 If \(\int_{0}^{a} \frac{d x}{4+x^{2}}=\frac{\pi}{8}\), then the value of \(a=\)

1 1
2 2
3 3
4 4
Integral Calculus

86402 The value of \(x\) that satisfies the equation \(\int_{\sqrt{2}}^{x} \frac{d t}{|t| \sqrt{t^{2}-1}}=\frac{\pi}{12}\) is

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

86403 \(\int_{1}^{e^{2}} \frac{\mathbf{d x}}{\mathbf{x}(1+\log x)^{2}}=\)

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

86399 \(\int_{0}^{3}\left|x^{2}-3 x+2\right| d x=\)

1 \(\frac{3}{2}\)
2 \(\frac{1}{6}\)
3 \(\frac{11}{6}\)
4 \(\frac{11}{2}\)
Integral Calculus

86400 If \(\int_{0}^{a} \frac{d x}{4+x^{2}}=\frac{\pi}{8}\), then the value of \(a=\)

1 1
2 2
3 3
4 4
Integral Calculus

86402 The value of \(x\) that satisfies the equation \(\int_{\sqrt{2}}^{x} \frac{d t}{|t| \sqrt{t^{2}-1}}=\frac{\pi}{12}\) is

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

86403 \(\int_{1}^{e^{2}} \frac{\mathbf{d x}}{\mathbf{x}(1+\log x)^{2}}=\)

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

86399 \(\int_{0}^{3}\left|x^{2}-3 x+2\right| d x=\)

1 \(\frac{3}{2}\)
2 \(\frac{1}{6}\)
3 \(\frac{11}{6}\)
4 \(\frac{11}{2}\)
Integral Calculus

86400 If \(\int_{0}^{a} \frac{d x}{4+x^{2}}=\frac{\pi}{8}\), then the value of \(a=\)

1 1
2 2
3 3
4 4
Integral Calculus

86402 The value of \(x\) that satisfies the equation \(\int_{\sqrt{2}}^{x} \frac{d t}{|t| \sqrt{t^{2}-1}}=\frac{\pi}{12}\) is

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

86403 \(\int_{1}^{e^{2}} \frac{\mathbf{d x}}{\mathbf{x}(1+\log x)^{2}}=\)

1 \(\frac{2}{3}\)
2 \(\frac{1}{3}\)
3 \(\frac{3}{2}\)
4 \(\log 2\)