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What is the difference between definite and indefinite integrals?

Definite integrals produces a numerical answer. It is asking the question: what is the area under the curve f(x) between x=a and x=b. Indefinite integrals produces a function. It is asking the question: what...
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Answered by Simeon H. • Maths tutor
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Differentiating (x^2)(sinx) Using the Product Rule

Firstly, what is the product rule? What does it actually say? Well, it tells us how to differentiate a function of the form uv - the product of the functions u and v. If y = uv, the product rule says: dy/dx ...
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Answered by Edward M. • Maths tutor
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Use the chain rule to differentiate y=(x-3)^(-3)

Hint: the chain rule states that for y=u(x) ^a, the derivative will be dy/dx = dy/du * du/dxSo we just need to find dy/du and du/dx!In this case u(x)=x-3, so du/dx = 1.from y=u^(-3), dy/du = -3u^(-4).This me...
RT
Answered by Rosemary T. • Maths tutor
5723 Views

Solve the inequality x < 4 - |2x + 1|.

In order to deal with the modulus sign, we must take account of 2 possible cases: Case 1: |2x + 1| = (2x +1). In this case we can solve algebraicly, preserving the inequality sign, to get that x &lt; 4 -(2x ...
JC
Answered by Joe C. • Maths tutor
8542 Views

Find the exact value of the gradient of the curve y = e^(2- x)ln(3x- 2). at the point on the curve where x = 2.

To solve this problem, we must first differentiate: Identify that we are able to use the product rule as our expression is of the form y = f(x)g(x) where f(x) = e^(2- x) and g(x) = ln(3x- 2). Hence f'(x) = -...
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Answered by Joe C. • Maths tutor
10607 Views