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What is the area bound by the x-axis, the lines x=1 and x=3 and the curve y=3x^(2)-1/x ? Answer in exact form.

Integrate, y= 3x²-1/x

1{³3x²- 1/x dx = [x-lnx]³₁= (3-ln3)-(1-ln1) = 3-ln3-1+0= 2-ln3

Answered by Escher L. • Maths tutor

4135 Views

Please explain the difference between compound and simple interest

First of all, let's start by defining the word 'interest'. Interest in mathematical terms generally means an amount of money that is accumulated over a period of time after an amount of money is invested ...

Answered by Henry M. • Maths tutor

4373 Views

f(x)=x^3 + x^2 -10x +8 show that (x-1) is a factor of f(x), Factorise f(x) fully , sketch the graph of f(x)

f(1)=0

f(x)=(x-1)(x+4)(x-2)

Answered by Deborah A. • Maths tutor

6199 Views

Make a the subject of: (a+3)=(2a+7)/r

Equation: a+3 = (2a+7)/r

First, we want to rearrange the equation, so that the 'r', which is the denominator of the right hand side, multiplies with (a+3), creating r(a+3) = 2a+7. ...

Answered by Jana M. • Maths tutor

13601 Views

Given that y = 4x^3 – 5/(x^2) , x =/= 0, find in its simplest form dy/dx.

We are given: y = 4x^3 – 5/(x^2) To find the dy/dx we are going to use the power rule, from the power rule differentiating x^n gives n*x^n-1, so from our equation differetiating x^3 will give 3x^2, but w...

Answered by Mohamed A. • Maths tutor

5510 Views