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Why is the integral of a function the area?

Say you have two functions, A and B, and A is the gradient of B. That is to say, A is as high as B is steep (at any point). Equally, A is as high as the rate of change of B (at any point). Now let’s say we w...
MC
Answered by Madison C. • Maths tutor
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How do we factorise an expression?

Step 1: Find the highest common factor of the terms in the expression eg. 3x+12 . In this expression 3 is the highest common factor of the terms 3x and 12 Step 2: Write the factor outside the brackets eg. 3x...
ML
Answered by Maria L. • Maths tutor
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Simplify p^2× p^5

The answer is P^7 because p is the same in both numbers and their powers need to be added up
AA
Answered by Alberto A. • Maths tutor
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integrate cos^2(x)*sin(x)

integral of cos 2 (x)*sin(x) we notice that we can use the spot the ball method here: Guessed integral: cos 3 (x) Differentiated Guessed Integral: -3sin(x)cos 2 (x), therefore our solution is (-1/3)*cos 3 (x)+c
CP
Answered by Cezar P. • Maths tutor
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If a=2 and b=3 , find the value of 2(a−b)+3(a+b)

My explanation would depend on the level of understanding of the person but one way would be the following: We know that a = 2. Substitute the value of "a" in the given equation: 2(2-b)+3(2+b) We k...
AC
Answered by Andrea C. • Maths tutor
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