Thursday

September 18, 2014

September 18, 2014

Posted by **Carmen** on Thursday, March 4, 2010 at 2:03am.

1) definite integral x/(1+x^4)dx b/w 0_infinity

2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity

3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity

4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity

Which of these integrals converge. First of all, what does it mean "converge"? How do you compare to "pure" powers of x?

How would you compute the exact value of at least one of the convergent integrals?

thanks

- calculus -
**bobpursley**, Thursday, March 4, 2010 at 8:47amexamine the powers.

4) x^4 dx is an x^5 in the numerator, an x^4 in the denominator. It cant converge to a finite value at inf.

1,2) definitely do, they converge to zero at inf

3) Think on that.

- calculus -
**Dana**, Wednesday, March 10, 2010 at 11:27amdo you do u substitution for each or automatically trig substitution. Because when you do trig sub you get 0 but when you do u sub then you get pi/4

**Answer this Question**

**Related Questions**

calculus - There are four integrals: 1) definite integral x/(1+x^4)dx b/w ...

Calc - If we know that the definite integral from -6 to -3 of f(x) equals 6, the...

definite integral - Use the Riemann Sums corresponding to 5 inscribed rectangles...

Calculus - Can someone explain to me how to do these? Given the following ...

Calculus - Would someone clarify this for me... Is antiderivatives just another ...

Calculus - Solve these indefinite and definite integrals. [integration sign] 4j-...

math - Note: You can get full credit for this problem by just answering the last...

Help W/ Definite Integrals - Evaluate the definite integral of (4x^3-x^2+2) from...

Calculus - "Leave the answer as a definite integral, but indicate how it could ...

Calculus II/III - A. Find the integral of the following function. Integral of (x...