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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 askin...

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 = u...

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...

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...

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-...