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# For any b > 0, compute the definite integral (2x/(1+x^2)) dx. Limits are 0 to b. Your answer will depend on b.?

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• For any b > 0, compute the definite integral (2x/(1+x^2)) dx. Limits are 0 to b. Your answer will depend on b.?

## Answers

... u&=&x^2-1\\ du&=&2x\, dx. \end{eqnarray*} Then \[ \int 2x(x^2-1)^4\, dx ... compute a definite integral ... 0 xe^{x^2}\, dx=\int^4_0 \frac{1 ...
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Positive: 34 %
The Indefinite Integral is: ∫ 2x dx = x 2 + C. At x=1: ... The Definite Integral, from 0 to 1, of sin(x) dx: ... a and b is the Indefinite Integral at b ...
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Positive: 31 %

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consider the deﬁnite integral Z b a f(x)dx. ... Z b a f(x)dx ≈ (y 0 +y 1)∆x 2 + (y 1 +y 2) ... ∆x 2 which simpliﬁes to the trapezoidal rule ...
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Positive: 34 %
Integration by substitution ... (x− 2)3dx (b) Z 1 0 (x+5)4dx (c) Z (2x− 1) ... Suppose now we wish to ﬁnd the integral Z 2x √ 1+x2 dx (3)
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Positive: 29 %
Calculus Facts Derivative of an Integral ... actually compute the definite integral and take its derivative. ... the answer is valid for any x > 0; ...
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Positive: 15 %
1 0 e 2x dx; and K= Z 1 1 ... B(t) = Z 1 0 e t 2(1+x ) 1 + x2 dx; we have A0(t) ... THE GAUSSIAN INTEGRAL 5 Note 1 2 = Z 1 0 p te t dt t = 1 0 e t p t dt ...
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Positive: 10 %

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