Calculus

Use the integral identity:
∫(a-1) (1/(1+x^2))dx=∫(1-1/a) (1/(1+u^2))du
for a>1 to show that:
arctan(a)+arctan(1/a)=π/2

  1. 0
  2. 0
  3. 0
asked by Andre
  1. after the integration, you have

    arctan(1) - arctan(a) = arctan(1/a) - arctan(1)

    π/4 - arctan(a) = arctan(1/a) - π/4

    rearrange the terms and you're done.

    1. 0
    2. 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. calc

    also: integral of tan^(-1)y dy how is integration of parts used in that? You write: arctan(y)dy = d[y arctan(y)] - y d[arctan(y)] Here we again have used the product rule: d(fg) = f dg + g df You then use that: d[arctan(y)] =
  2. calculus

    Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is? It's 3/2 but I am not very clear on how to obtain the answer. I changed arctan x/2 into dy/dx=(4-2x)/(4sqrt(4+x^2)) but that's as far as I got.
  3. Math

    Arrange these in order from least to greatest: arctan(-sqrt3), arctan 0, arctan(1/2) So far I got the first two values, arctan(-sqrt3), and that's 150 degrees. Arctan 0 would be zero degrees. I'll use just one answer for now, but
  4. calculus

    h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ? -> using u=1/x, we can write h(x)= integral from (1, 1/x) arctan (2t)dt as h(u)= integral from (1,u) arctan(2t)dt and h'(u)= arctan (2) Part 2: By the chain
  5. calculus

    h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ? -> using u=1/x, we can write h(x)= integral from (1, 1/x) arctan (2t)dt as h(u)= integral from (1,u) arctan(2t)dt and h'(u)= arctan (2) Part 2: By the chain
  6. Calculus

    Note that pi lim arctan(x ) = ---- x -> +oo 2 Now evaluate / pi \ lim |arctan(x ) - -----| x x -> +oo \ 2 / I'm not exactly sure how to attempt it. I have tried h'opital's rule but I don't believe you can use it here. Any help
  7. precal

    The values of x that are solutions to the equation cos^(2)x=sin2x in the interval [0, pi] are a. arctan(1/2) only b. arctan(1/2) and pi c. arctan(1/2) and 0 d. arctan(1/2) and (pi/2) e. arctan(1/2), o, and (pi/2)
  8. Calculus prince@18

    let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of
  9. calculus

    Now we prove Machin's formula using the tangent addition formula: tan(A+B)= tanA+tanB/1-tanAtanB. If A= arctan(120/119) and B= -arctan(1/239), how do you show that arctan(120/119)-arctan(1/239)=arctan1?
  10. Calc

    Evaluate the integral (3x+4)/[(x^2+4)(3-x)]dx a. (1/2)ln(x^2+4) + ln|3-x| + C b. (1/2)arctan(x/2) + ln|3-x| + C c. (1/2)arctan(x/2) - ln|3-x| + C d. ln|(sqrt(x^2+4)/(3-x))| + C e. None of the above

More Similar Questions