Integration help needed!! (1 Viewer)

[RHINO7]

Please need help with these questions:

i) Indefinite integral of x 1/3 dx



ii) Indefinite integral of 3/x^2 dx



iii) Indefinite integral of (t^2-4)(t-1) dt

 

[SoulSearcher]

i) Should be very simple, assuming it's x/3
ii) Convert 3/x² into 3x^-2 then integrate from there
iii) Expand the brackets, then integrate as normal.

 

[PC]

(i) Indefinite integral of x 1/3 dx
I'm assuming this is x^1/3, so the integral is (3/4)x^4/3 + C.

(ii) Indefinite integral of 3/x^2 dx
I'm assuming this is 3/x² which is 3x^-2. The integral is –3x^-1 + C.

(iii) Indefinite integral of (t^2-4)(t-1) dt
I'm assuming this is (t² – 4)(t – 1). Best to expand first.
You get t³ – t² – 4t + 4.
The integral is (1/4)t⁴ – (1/3)t³ – 2t² + 4t + C.

IN GENERAL, to integrate terms of the form xⁿ,
1. Add one on to the index
2. Differentiate back to check

 

[watatank]

(ii) Indefinite integral of 3/x^2 dx
I'm assuming this is 3/x² which is 3x^-2. The integral is –3x^-1 + C.

slight mistake its –3x^-3 + C.

 

[SoulSearcher]

slight mistake its –3x^-3 + C.

That's the process for getting the derivative :uhhuh: Even so, the derivative would be -6x^-3.

 

[watatank]

That's the process for getting the derivative :uhhuh: Even so, the derivative would be -6x^-3.

Hahahaha yep that'll teach me for attempting to fix things up. <sigh>

 

[PC]

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