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Find the exact value of the integral of (2+7/x), between x=1 and x=e. Give your answer in terms of e.

1.) Find the integral of each term. --> [2x +7ln(x)]. --> Uses standard integrals--> e.g. that the integral of 1/x is ln(x).
2.) substitute values into the integral. --> [2(e)+ 7ln(e)]-...

Answered by • Maths tutor

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Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)

Base case - First let us consider the base case where n=1. Then the left hand side of the equation becomes 1 and the right hand side is (1/6)12*3=6/6=1. Thus LHS=RHS and we are d...

Answered by Anna R. • Further Mathematics tutor

5168 Views

Expand (x+4)(x-4)=33 to give values of x

Use FOIL to expand the brackets. To do this, we start by multiplying the FIRST value in each bracket which in this case is x so we get x^2. Then we multiply the OUTSIDE two values, so here that is x and -...

Answered by Aria B. • Maths tutor

3224 Views

How do surds relate to powers and roots?

To understand surds we have to understand powers and there uses. So to start we should look at powers such as what is 2² , 3², and 5². This shows us going up but then we l...

Answered by Alistair G. • Maths tutor

2906 Views

Describe the structure and function of a chloroplast

Chloroplasts are organelles found only in plants that allow the plant to release energy from sunlight through photosynthesis. They are green in colour because they contain the pigment chlorophyll.

Answered by Joy B. • Biology tutor

4283 Views