4u integration! (1 Viewer)

[sakurali823]

just needed help for a few questions, thanks =)

1) 1
] x^3/x^2+x+1 dx
0

2)a) express the derivative of loge(secx+tanx)as a single trigonometric ratio.
b)hence find an indefinite integral of ]dx/(a^2+x^2)^1/2

3)]dx/(x^1/2)(1-x^1/2)^1/2

4)]lnx/x dx

5)]sin^4x dx
6)]sec^2x tanx dx
7)]tan^3x dx

8)]cos^2x.sin^4x dx
9)]cos^3x.sin^2x dx

10)]2x/16+x^4 dx

 

[pLuvia]

1 I'm guessing you meant x³/(x²+x+1), use long division to make the fraction much more simpler and then you can integrate it

2.
a) Simple differentiation
b) Use the result of a) quite easy when you see it

3. Let u=sqrt(1-x^1/2)

4. Let u=lnx

5. You can use the double angle formulae

6. Let u=tanx

7. Let u=secx

Similar for 8 and 9

10. Let u=x²

 

[blakwidow]

just needed help for a few questions, thanks =)

1) 1
] x^3/x^2+x+1 dx
0

2)a) express the derivative of loge(secx+tanx)as a single trigonometric ratio.
b)hence find an indefinite integral of ]dx/(a^2+x^2)^1/2

3)]dx/(x^1/2)(1-x^1/2)^1/2

4)]lnx/x dx

5)]sin^4x dx
6)]sec^2x tanx dx
7)]tan^3x dx

8)]cos^2x.sin^4x dx
9)]cos^3x.sin^2x dx

10)]2x/16+x^4 dx

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Sry im new to the site and its a bit hard for me to read some of the symbols. These questions are quite tough and you should know 3 unit integration quite well and also integration by parts.

Ill have a go at

tan^3x dx

= tanx. tan^2x dx
=tanx (sec^2 -1) dx

= S (tanx sec^2 x) dx - S (tanx) dx

= S tanx d(tanx) - S tanx dx

=1/2tan^2x + ln|cos x| + c

Do you know of any program which can type mathematically symbols so I can copy/paste onto this site?

-blakwidow

 

[pLuvia]

You can try using the MS word one or use the VB codes

Superscript - [sup ]text[/sup] = ^text

Subscript - [sub ]text[/sub] = _text

Without the space in the ^and

 

[alcalder]

∫ √ ≥ * ≤ ∆ ∑ п ≈ ∞

If you are using Windows, just use the Character Map in the Accessories/System Tools.

This font is Verdana. Many other fonts also have these "add-on" maths symbols.

Hope that helps.

 

[blakwidow]

ok thanks

 

[Affinity]

demand LaTeX support.

 

[Slidey]

Bug pLuvia about it, Affinity. My requests in the mod forum always fell on deaf ears, perhaps he'll have more luck!