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Integrating cos^2(x)+5sin^2(x)

Firstly, note that cos^2(x)+5sin^2(x)= cos^2(x) +sin^2(x) +4sin^2(x). By trignoemtric identies, cos^2(x)+sin^2(x)=1 and so we can just integrate 1+4sin^2(x) since this is equal to cos^2(x)+5sin^2(x). Again, ...
RL
Answered by Rafe L. • Maths tutor
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Find the all the angles of a triangle with side lengths of 8cm, 11cm and 11cm.

Using the knowledge of a 2 = b 2 + c 2 - 2bcCos(A) Rearrange to aquire Cos(A) = (b 2 + c 2 - a 2 )/2bc Then input the values to obtain the angles of 42, 69, 69.
AJ
Answered by Alexander J. • Maths tutor
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Differentiate with respect to x: 4(x^3) + 2x

d/dx(4x 3 + 2x) = d/dx (4x 3 ) + d/dx(2x) = 4(3x 2 ) + x = 12x 2 + x
AJ
Answered by Alexander J. • Maths tutor
5701 Views

How do I add up the integers from 1 to 1000 without going insane?

Suppose you are asked by your teacher to sum all the integers from 1 up to 1000. You might be thinking they must hold some kind of grudge against you. If you try to calculate the sum by adding on each intege...
MB
Answered by Matthew B. • Maths tutor
7892 Views

Differentiate y=(4x - 5)^5 by using the chain rule.

Notation: I use the ^ in the title question to indicated 'to the power of' and I use an asterisk * (or star) to indicate 'multiplied by' in the answer, to avoid confusion with the x term! Step 1) let u = 4x ...
JE
Answered by Joseph E. • Maths tutor
13822 Views