Question

Integrate 6x/(sin^2x) from pi/6 , pi/2

Answer 1

why don't you plug in the values and see what result you get?

Answer 2

how to do integral of 6x/(sin^2x)

Answer 3

http://www.mathsisfun.com/calculus/integration-rules.html

Answer 4

x is not constant how we can take it out....

Answer 5

Use should use uv substitution for this

Answer 6

ok ..thanks

Answer 7

sorry, didn't read your question properly.
i agree with Hero, use integration by substitution

Answer 8

yes by parts, or if u knw complex numbers, consider complexifying....

Answer 9

\[I:=\int \dfrac{6x}{\sin^2x}dx\]\[= \int 6x \cdot \dfrac{1}{\sin^2x}dx\]\[= \int 6x\cdot \csc^2(x)dx\]
\[u = 6x \Rightarrow du = 6dx\]\[v = -\cot(x) \Rightarrow dv = \csc^2(x) dx\Rightarrow \]
Now,\[I=uv - \int vdu\]\[=-6x\cot x -\int -6\cot(x)dx\]\[= -6x\cot x +6\ln|\sin(x)|+C\]

Answer 10

I have no idea why it took so long to submit.

Answer 11

Anyway, that's the antiderivative.