How will I solve this without substitution?

Question

How will I solve this without substitution?

The integral is $(1 + {sin}^{2} θ csc θ) d θ$ $(1 + sin^2theta csctheta)d theta$

2 Answers

Impact of this question

1038 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-05T20:32:50

Simplify using standard trig definitions

Explanation:

Recall the definition of $csc$ $csc$ as $csc θ = \frac{1}{sin θ}$ $csctheta=1/sintheta$ . So this expression simplifies to be $\int 1 + sin θ d θ = θ - cos θ + C$ $int1+sinthetad theta=theta-costheta+C$

Answer 2 · 2018-06-05T20:35:43

See explanation.

Explanation:

According to the definition of $csc θ$ $csc theta$ we have:

$csc θ = \frac{1}{sin θ}$ $csc theta=1/sintheta$

If we use this identity, then the integral is:

$\int (1 + \frac{{sin}^{2} θ}{sin θ}) d θ = \int (1 + sin θ) d θ = θ - cos θ + C$ $int (1+sin^2theta/sintheta)d theta= int(1+sintheta)d theta=theta -cos theta+C$

Science

Math

Humanities

... and beyond

How will I solve this without substitution?

The integral is $(1 + {sin}^{2} θ csc θ) d θ$ $(1 + sin^2theta csctheta)d theta$

2 Answers

Explanation:

Explanation:

$csc θ = \frac{1}{sin θ}$ $csc theta=1/sintheta$

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How will I solve this without substitution?

The integral is (1+sin2θcscθ)dθ(1 + sin^2theta csctheta)d theta

2 Answers

Explanation:

Explanation:

cscθ=1sinθcsc theta=1/sintheta

Related questions

Impact of this question

The integral is $(1 + {sin}^{2} θ csc θ) d θ$ $(1 + sin^2theta csctheta)d theta$

$csc θ = \frac{1}{sin θ}$ $csc theta=1/sintheta$