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How to integrate ∫〖3x/√(1-x^2 ) dx〗?

We will use integration by substitution to solve this integral. Let 1-x^2=sin^2(u) This means that: x^2=1-sin^2(u)=cos^2(u) (using the trigonometric identity sin^2(x)+cos^2(x)=1). Therefore, x=cos(u). If we ...
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Answered by Alma O. • Maths tutor
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The velocity of a particle is given by the equation v= 4t+cos4t where t is the time in seconds and v is the velocity in m s ^-1. Find the time t when the particle is no longer accelerating for the interval 0≤t≤2.

This problem tests two key sub-topics in calculus, kinematics and the chain rule. Firstly, you must realise that the derivative of a velocity function will give you the acceleration function. So by finding t...
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Answered by Marc B. • Maths tutor
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Given the function y=f(x), where f(x)=(e^x-e^(-x))/2, find its inverse f'(x).

This is a very common IB-level question, which is solved with using the technique of a "disguised quadratic". The first thing we want to do in finding the inverse is swapping the places of x and y ...
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Answered by Edoardo M. • Maths tutor
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What does it take to make a 7 in HL Math?

A question that haunts every IB HL Math student day and night. Most students beleive that if they solve all past exams and practice book problems they should easily make a seven. That is absolutely not true....
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Answered by Youssef M. • Maths tutor
16789 Views

Find the coordinates that correspond to the maximum point of the following equation: y = −16x^2 + 160x - 256

To solve this problem, the maximum and minimum points of equations can be deduced through the differentiation process. This looks at the gradient of the function and the maximum/minimum value occurs when the...
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Answered by Michael W. • Maths tutor
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