Calculus
posted by Andre .
Use the integral identity:
∫(a1) (1/(1+x^2))dx=∫(11/a) (1/(1+u^2))du
for a>1 to show that:
arctan(a)+arctan(1/a)=π/2

Calculus 
Steve
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.
Respond to this Question
Similar Questions

calculus
Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is? 
calc
also: integral of tan^(1)y dy how is integration of parts used in that? 
Math integrals
What is the indefinite integral of ∫ [sin (π/x)]/ x^2] dx ? 
calculus
h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ? 
calculus
h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ? 
Calculus 2 correction
I just wanted to see if my answer if correct the integral is: ∫(7x^3 + 2x  3) / (x^2 + 2) when I do a polynomial division I get: ∫ 7x ((12x  3)/(x^2 + 2)) dx so then I use u = x^2 + 2 du = 2x dx 1/2 du = x dx = ∫7x … 
Integral Calculus
Trying to find ∫x*arctan(x)dx, but I can't figure out what do to after: (1/2)x^2*arctan(x)1/2∫x^2/(x^2+1) dx 
physics
1.∫ csc (uπ/2) cot (uπ/2) du. 2.∫ sec^2(3x+2)ds 3.∫ √32s ds 4. ∫ 12(y^4+y4y^2+1)^2 (4^3+2y) dy use u= y^4+4y^2+1 
Calculus
Alright, I want to see if I understand the language of these two problems and their solutions. It asks: If F(x) = [given integrand], find the derivative F'(x). So is F(x) just our function, and F'(x) our antiderivative? 
Calculus III
Use symmetry to evaluate the double integral ∫∫R(10+x^2⋅y^5) dA, R=[0, 6]×[−4, 4]. (Give your answer as an exact number.) ∫∫R(10+x^2⋅y^5) dA=