evaluate the following integrals, showing all working

a) int((sec^3*3x)(tan3x)) dx

b)int((sin15x)(cos9x)) dx

I was alright until the trig questions, could someone please get me started on these two.

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- May 14th 2008, 07:28 AMsamdmansamtrigonometric integration
evaluate the following integrals, showing all working

a) int((sec^3*3x)(tan3x)) dx

b)int((sin15x)(cos9x)) dx

I was alright until the trig questions, could someone please get me started on these two. - May 14th 2008, 07:43 AMmr fantastic
- May 14th 2008, 10:36 AMSoroban
He4llo, samdmansam!

Another approach to (a) . . .

Quote:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

When we have: .

. . there is a procedure we can follow.

There are three cases to consider . . .

[1] Even secant, any tangent.

Example: .

We have: .

. . . . . . . . . .

. . . . . change to tangents

. . . . . . . . .

. .

. . And we have: .

[2] Odd tangent, any secant

Example: .

We have: .

. . . . . . . . . . . . . .

. . . . . . . . . change to secants

. . . . . . . . . . . .

. .

. . And we have .

[3] Odd secant, even tangent

This is the dreaded case, where a formula must be known

. . or it must be derived.

. .

and a reduction formula is also recommended.