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What is the difference between a definite integral and an indefinite integral?

A definite integral is actually a numerical value, which the represents the area under a graph between two points. For example, if you integrated f(x) between two values (lets call them a and b), the answer ...
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Answered by Alex W. • Maths tutor
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G(x)=x^3 + 1, h(x)=3^x; solve G(h(a))=244

First combine the two functions so that we have an equation for a to solve: G(h(a)) = (3^x)^3 + 1 = 3^(3x) + 1 = 244 which gives 3^(3x) = 243 Now we can use logarithms in order to solve the equation log(3^(3...
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Answered by Josephine S. • Maths tutor
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Find the tangent to the curve y = x^2 + 3x + 2 at x = 1

First, we differentiate y = x^2 + 3x + 2 to find the slope of the curve at any given x point: dy/dx = 2x + 3 So at x = 1, dy/dx = 2 + 3 = 5 We know that straight lines come in the form y = mx + c, and in thi...
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Answered by Samuel B. • Maths tutor
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Differentiate: y = sin(2x).

Using the chain rule with u = 2x: y = sin(2x) becomes y = sin(u) dy/dx = dy/du * du/dx dy/du = cos(u) du/dx = 2 So dy/dx = dy/du * du/dx = 2 cos(u).
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Answered by Samuel B. • Maths tutor
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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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