calculus
posted by anonymous .
calculate the indefinite integral
2sec^2x dx
(cosx)/(sin^3x) dx
calculate the definite integral
interval pi/4, pi/12
csc2xcot2x dx

Well, I happen to know that the derivate of the tangent is sec^2 :)
(cosx)/(sin^3x) dx
Try f(x) = 1/sin^2 x
f' =  2 sin x cos x /sin^4 x
see what happens?
let u = 2 x
then du = 2 dx
and we have
csc u cot u du/2 from u = pi/2 to pi/6
(1/sin u)(cos u/sin u) du/2
= (1/2) (cos u/sin^2 u) du
try 1/sin u
Respond to this Question
Similar Questions

Calculus
Solve these indefinite and definite integrals. [integration sign] 4j5j^3 dj I got 2j^2  5/4j^4... is this my final answer? 
Calculus
Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of (sin(3*pi*t))dt For this one, I got 1/3pi cos (9 pi^2) + 1/3pi 2. indefinite integral of sinxcos(cosx)dx I got sin(cosx) + C 3. Indefinite integral of x over (root … 
Calculus II/III
A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the xaxis from 4 to 9. For part … 
Integral
That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = cos x du = cos x dx The integral is u v  integral of v du = sinx cosx + integral of cos^2 dx which can be rewritten integral … 
calculus
calculate the indefinite integral (cosx)/(sin^3x) 
Calculus
Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each definite integral. (a) Integral of sinx*dx from pi/4 to pi/4 (b) Integral of cosx*dx from pi/4 to pi/4 (c) Integral of cosx*dx from pi/2 … 
Calc BC
1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2(pix/7)dx 2. Find the indefinite integral by making the substitution x=3tan(theta). Indefinite integral x*sqrt(9+x^2)dx 3. Find the indefinite integral. Indefinite … 
Calculus (urgent help)
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: … 
calculus
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: … 
calculus (please with steps and explanations)
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: …