Definite Integral as Limit of a Sum
Integral Calculus

86445 The value of \(\int_{0}^{2} \frac{x^{2}}{\left(x^{3}+1\right)^{2}} d x\) is equal to

1 \(\frac{1}{27}\)
2 \(\frac{5}{27}\)
3 \(\frac{7}{27}\)
4 \(\frac{8}{27}\)
5 \(\frac{1}{3}\)
Integral Calculus

86446 The value of \(\int_{0}^{\sqrt{3}} \frac{6}{9+x^{2}} d x\) is equal to

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

86447 \(\int_{0}^{\pi / 2} \frac{1}{1+\cot ^{4} \mathrm{x}} \mathrm{dx}=\)

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(\frac{\pi}{8}\)
5 \(2 \pi\)
Integral Calculus

86448 \(\int_{-1}^{0} \frac{d x}{x^{2}+2 x+2}\) is equal to

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

86449 If \(\int_{0}^{x} f(t) d t=x^{2}+e^{x}(x>0)\), then \(f(1)\) is equal to

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

86445 The value of \(\int_{0}^{2} \frac{x^{2}}{\left(x^{3}+1\right)^{2}} d x\) is equal to

1 \(\frac{1}{27}\)
2 \(\frac{5}{27}\)
3 \(\frac{7}{27}\)
4 \(\frac{8}{27}\)
5 \(\frac{1}{3}\)
Integral Calculus

86446 The value of \(\int_{0}^{\sqrt{3}} \frac{6}{9+x^{2}} d x\) is equal to

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

86447 \(\int_{0}^{\pi / 2} \frac{1}{1+\cot ^{4} \mathrm{x}} \mathrm{dx}=\)

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(\frac{\pi}{8}\)
5 \(2 \pi\)
Integral Calculus

86448 \(\int_{-1}^{0} \frac{d x}{x^{2}+2 x+2}\) is equal to

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

86449 If \(\int_{0}^{x} f(t) d t=x^{2}+e^{x}(x>0)\), then \(f(1)\) is equal to

1 \(1+\mathrm{e}\)
2 \(2+\mathrm{e}\)
3 \(3+\mathrm{e}\)
4 e
5 0
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Integral Calculus

86445 The value of \(\int_{0}^{2} \frac{x^{2}}{\left(x^{3}+1\right)^{2}} d x\) is equal to

1 \(\frac{1}{27}\)
2 \(\frac{5}{27}\)
3 \(\frac{7}{27}\)
4 \(\frac{8}{27}\)
5 \(\frac{1}{3}\)
Integral Calculus

86446 The value of \(\int_{0}^{\sqrt{3}} \frac{6}{9+x^{2}} d x\) is equal to

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

86447 \(\int_{0}^{\pi / 2} \frac{1}{1+\cot ^{4} \mathrm{x}} \mathrm{dx}=\)

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(\frac{\pi}{8}\)
5 \(2 \pi\)
Integral Calculus

86448 \(\int_{-1}^{0} \frac{d x}{x^{2}+2 x+2}\) is equal to

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

86449 If \(\int_{0}^{x} f(t) d t=x^{2}+e^{x}(x>0)\), then \(f(1)\) is equal to

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

86445 The value of \(\int_{0}^{2} \frac{x^{2}}{\left(x^{3}+1\right)^{2}} d x\) is equal to

1 \(\frac{1}{27}\)
2 \(\frac{5}{27}\)
3 \(\frac{7}{27}\)
4 \(\frac{8}{27}\)
5 \(\frac{1}{3}\)
Integral Calculus

86446 The value of \(\int_{0}^{\sqrt{3}} \frac{6}{9+x^{2}} d x\) is equal to

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

86447 \(\int_{0}^{\pi / 2} \frac{1}{1+\cot ^{4} \mathrm{x}} \mathrm{dx}=\)

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(\frac{\pi}{8}\)
5 \(2 \pi\)
Integral Calculus

86448 \(\int_{-1}^{0} \frac{d x}{x^{2}+2 x+2}\) is equal to

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

86449 If \(\int_{0}^{x} f(t) d t=x^{2}+e^{x}(x>0)\), then \(f(1)\) is equal to

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

86445 The value of \(\int_{0}^{2} \frac{x^{2}}{\left(x^{3}+1\right)^{2}} d x\) is equal to

1 \(\frac{1}{27}\)
2 \(\frac{5}{27}\)
3 \(\frac{7}{27}\)
4 \(\frac{8}{27}\)
5 \(\frac{1}{3}\)
Integral Calculus

86446 The value of \(\int_{0}^{\sqrt{3}} \frac{6}{9+x^{2}} d x\) is equal to

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

86447 \(\int_{0}^{\pi / 2} \frac{1}{1+\cot ^{4} \mathrm{x}} \mathrm{dx}=\)

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(\frac{\pi}{8}\)
5 \(2 \pi\)
Integral Calculus

86448 \(\int_{-1}^{0} \frac{d x}{x^{2}+2 x+2}\) is equal to

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

86449 If \(\int_{0}^{x} f(t) d t=x^{2}+e^{x}(x>0)\), then \(f(1)\) is equal to

1 \(1+\mathrm{e}\)
2 \(2+\mathrm{e}\)
3 \(3+\mathrm{e}\)
4 e
5 0