How do you antidifferentiate this equation?

[iVincent]

Can anyone show me how to antiderive this equation? This question is taken from the VCAA exam Methods (CAS) Exam 1 2012, Q9b.

[brightsky]

Integration by parts.

int x cosx dx
= int d/dx (sinx) x dx
= x sinx - int sinx d/dx (x) dx
= x sinx - int sinx dx
= x sinx + cosx + c

[Floatzel98]

Just a bit confused, i thought integration by parts was not in the Methods SD, let alone Specialist. How would we know how to answer that, especially if it's on Exam 1 (Non-Calc)?

[keltingmeith]

Just a bit confused, i thought integration by parts was not in the Methods SD, let alone Specialist. How would we know how to answer that, especially if it's on Exam 1 (Non-Calc)?

This is the exam in question. As you can see, the first part of this was a set-up so that you knew how to do it. They even say in the first part of the question to use your result from part a (in bold, even)

[Floatzel98]

This is the exam in question. As you can see, the first part of this was a set-up so that you knew how to do it. They even say in the first part of the question to use your result from part a (in bold, even)

Ah okay. That makes a lot more sense. That makes it an integration by recognition question then, yes?

[pi]

Ah okay. That makes a lot more sense. That makes it an integration by recognition question then, yes?

Do the question and find out

[Floatzel98]

It might out be set out the best, but is the working okay, (if you can actually see it)? I checked the examiners report and the answers is the same

[keltingmeith]

It might out be set out the best, but is the working okay, (if you can actually see it)? I checked the examiners report and the answers is the same

When you've jumped to calculation of the definite integral, as long as you also write the actual definite integral, that working should be perfect.