Question

Evaluate integral

Answer 1

How do u use fundamental theorem of calculus in here?

Answer 2

@sirm3d Plz come when u are here >.> so sorry for having so many ques @@

Answer 3

see integral of the question u posted is
1/3(pi) * (-csc(3pi)t)
and hence the reqd ans is
1/3(pi) *( (-csc(3pi)/6) -(-csc(3pi)/18)=1/3(pi) *(-1+2)=1/3(pi)

Answer 4

no idea what u are saying.. 1/3 pi is the answer , not part of the quesiton

Answer 5

integral of csc(3pi)t*cot (3pi)t =1/3(pi) * (-csc(3pi)t)
in this answer for t u first substitute the upper limit and the n for t u substitute the lower limit and then just subtract the two results..

Answer 6

i actually need an explanation more than the work, cuz i got the solution as well.

Answer 7

@matricked how is this related to fundamental theorem of cal I?

Answer 8

becoz of fundamental theorem we are substituing the two limits and then subtracting the result
here we don't write integral constant
for the theorem u cn consult any book on integral calculus or any website will do

Answer 9

I looked on a website , it just says F'(x) = f(x)

Answer 10

and how u get csc u

Answer 11

how did u go from csc u cot u to csc u

Answer 12

integral of F'(x) = f(a) -f(b) where a and b are the upper and lower limits and F'(x) = f(x)

Answer 13

that's the formula of integral of csc u cot u is -csc u

Answer 14

ah, ok thanks

Answer 15

welcome dear

Answer 16

there are two fundamental theorems of calculus.

(1) connects derivative and integral - integral calculus was developed independently from differential calculus, but it turns out that integration is the reverse process of differentiation

(2) evaluating a definite integral without using the Riemann sum.