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Maths
A Level

Evaluate the indefinite integral: ∫ (e^x)sin(x) dx

Note: for what’s about to come, ' denotes derivative with respect to x. Method 1 (integration by parts): let I = (e^x)sin(x) dx let u = sin(x)...

Answered by ShenZhen N. Maths tutor
11779 Views

How do I find the area under a curve between two points?

Assuming you know the equation of the line, this could possibly be done in several ways. If you are able to integrate the equation of the line definitely using your current knowledge, then do this between...

Answered by Reece R. Maths tutor
4341 Views

What is the point of differentiation?

Differentiation is a very useful concept; informally it tells us how 'fast' something is changing. A real-life example is given by the first and second derivatives of distance with respect to time: the fi...

Answered by Jake H. Maths tutor
9285 Views

A factory produces cartons each box has height h and base dimensions 2x, x and surface area A. Given that the capacity of a carton has to be 1030cm^3, (a) Using calculus find the value of x for which A is a minimum. (b) Calculate the minimum value of A.

To calculate the minimum value of A we first need to establish an equation for A. The surface area of a cuboid is relatively simple to figure out we simply work out the area of the faces and sum them toge...

Answered by Jacob C. Maths tutor
3928 Views

Solve the simultaneous equations y + 4x + 1 = 0 and y^2 + 5x^2 + 2x = 0

y=-4x-1
(-4x-1)^2 +5x^2 +2x=0

16x^2 +8x +1 +5x^2 +2x=0

21x^2 +10x + 1 =0
(7x+1)(3x+1)=0

x=-1/7 or -1/3

y= -3/7 or 1/3

Answered by Dinesh J. Maths tutor
13793 Views

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