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A curve has equation y = f(x) and passes through the point (4, 22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7, use integration to find f(x), giving each term in its simplest form

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term in...
AC
Answered by Alex C. • Maths tutor
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How do you integrate ln(x)?

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a special c...
OD
Answered by Omkar D. • Maths tutor
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Find the constant term in the expression (x^2-1/x)^9

This problem uses the binomial expansion formula: (x+y) n = k=0 Z n n C k x k y n-k .But lets try to understand where this formula comes from by doing the problem without it to start of with.We have the expr...
VY
Answered by Vincent Y. • Maths tutor
8045 Views

Differentiate: tan(2x) cos(x)

Explain the product rule : d/dx ( f(x) . g(x) ) = f'(x).g(x) = g'(x) . f (x) 2. Briefly run through trigonometric derivatives .* cos (x) differentiates to: -sin(x)* tan (x) differentiates to: sec^2 (x) 3. Br...
SD
Answered by Shreyasi D. • Maths tutor
7183 Views

Rationalise the fraction : 5/(3-sqrt(2))

To rationalise a fraction we have to eliminate the surds in the denominator. We know we can multiply the top and the bottom of a fraction by the same thing, as this is equivalent to multiplying by 1. Notice ...
MM
Answered by Michael M. • Maths tutor
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