Warning: Illegal string offset 'html' in /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php on line 909

1994 - Paper 1 - Question 4 - HSN forum

# 1994 - Paper 1 - Question 4

7 replies to this topic

### #1Ally

HSN Legend

• Moderators
• 2,912 posts
• Interests:Just finished 1st year at uni studying medicine.
• Gender:Male

Posted 20 May 2004 - 12:18 PM

Hi could someone help me with this question:

Differentiate sin³x with respect to x

Hence find ∫ sin²xcosx dx.

I know how to differentiate it, but I can't get the second part

The answer given is 1/3 sin³x

Could someone help...?

### #2Ally

HSN Legend

• Moderators
• 2,912 posts
• Interests:Just finished 1st year at uni studying medicine.
• Gender:Male

Posted 20 May 2004 - 12:26 PM

I think it's actually Question 17 and not Question 4

### #3james1

Top of the Class

• Members
• 334 posts

Posted 20 May 2004 - 12:30 PM

Is this for Higher.

It looks like a C level AH question using integration by substituiton.

### #4Ally

HSN Legend

• Moderators
• 2,912 posts
• Interests:Just finished 1st year at uni studying medicine.
• Gender:Male

Posted 20 May 2004 - 12:36 PM

Yeh its definately higher.

Any tips on how to working it out...?

### #5AndyW

Good Effort

• Members
• 65 posts
• Gender:Not Telling

Posted 20 May 2004 - 12:47 PM

I think this is beyond Higher level:

y = (sin x)^3

let u = sin x

dy/dx = dy/du du/dx
= 3(sin x)^2 * cos x

sin²xcosx dx

Note that the term you're integrating is just 1/3 of what you found dy/dx to be previously.

Therefore

sin²xcosx dx = 1/3 y = 1/3 (sin^3 x)

### #6Ally

HSN Legend

• Moderators
• 2,912 posts
• Interests:Just finished 1st year at uni studying medicine.
• Gender:Male

Posted 20 May 2004 - 12:52 PM

Is it?

It was the last question in the paper so maybe thats why it's so hard.

But still, hopefully no AH questions will come up 2morrow!

### #7Ally

HSN Legend

• Moderators
• 2,912 posts
• Interests:Just finished 1st year at uni studying medicine.
• Gender:Male

Posted 20 May 2004 - 01:00 PM

Did this used to be in the Old Higher Course?

If it is, then, maybe thats the disadvantage of doing the really old papers

### #8George

Child Prodigy

• 720 posts
• Location:West Lothian
• Gender:Male

Posted 20 May 2004 - 01:04 PM

I think it is just a hard Higher question.

I can't see anything specific in the current Arrangements, but you are basically being expected to notice that integrating sin²xcosx dx is related to what you previously worked out.

#### 1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users