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help with maths...am I just being really stupid??

Okay so I'm just working through the OCR Core 3 maths specimen paper, and to find the area under a curve I have to integrate (4x+1)^-1/2

Now I thought this would work out as 1/4 x 1/2(4x+1)^1/2 and therefore 1/8(4x+1)^1/2

But the answer scheme has it down as being 1/2(4x+1)^1/2

Is the answer scheme wrong or am I just being really thick? I am majorly hungover from a night out last night so the latter wouldn't surprise me tbh.

But I am aware that the specimen papers and answer schemes aren't as vigorously checked as real papers, so it is possible it's wrong.

Help is appreciated :smile:
Differentiate your answer and the mark scheme's answer, and you'll see the mistake you've made.
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Avatar for alexKS
alexKS
OP
Ohh yh I know what i did...I multiplied by the new power rather than the inverse. Thanks :smile:
Reply 3
Avatar for XShmalX
XShmalX
1
Original post by alexKS
Okay so I'm just working through the OCR Core 3 maths specimen paper, and to find the area under a curve I have to integrate (4x+1)^-1/2

Now I thought this would work out as 1/4 x 1/2(4x+1)^1/2 and therefore 1/8(4x+1)^1/2

But the answer scheme has it down as being 1/2(4x+1)^1/2

Is the answer scheme wrong or am I just being really thick? I am majorly hungover from a night out last night so the latter wouldn't surprise me tbh.

But I am aware that the specimen papers and answer schemes aren't as vigorously checked as real papers, so it is possible it's wrong.

Help is appreciated :smile:

If y=(4x+1)^1/2
so dy/dx=(1/2)*4*(4x+1)^(-1/2)=2(4x+1)^-1/2
So the integral of (4x+1)^-1/2 must be 1/2(4x+1)^1/2

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