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Use integration by parts to find ∫ (x^2)sin(x) dx. (A good example of having to use the by parts formula twice.)

Before we blindly start using the integration by parts formula, we can see that no matter how many times we differentiate or integrate sin(x) we will still have a trigonometric function. The aim of the 'b...

Answered by Jack C. • Maths tutor

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5x(3+2) =?

5 x(3+2) =5x(5)= 25

Answered by Harish C. • Maths tutor

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Find values for x and y from two simultaneous equations: 2x + y = 5 and 3x + y = 7

Rearrange one of the equations to make y the subject:y = 5 - 2x Substitute y into the other equation: 3x + 5 - 2x = 7 x = 2 y = 5 - (2 x 2) y = 1

Answered by Marco V. • Maths tutor

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Find the intergal of 2x^5 -1/(4x^3) -5 giving each term in its simplest form.

When integrating, we raise the power by 1 and divide by the new powerSo, 2x⁵ becomes 2x⁶ /6 which simplified down as the question asks is x^6/3-1/(4x³) is -(1/4)x^^-3<...

Answered by Emily W. • Maths tutor

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Barney has 12 items of fruit. Four of these are apples. If Lucy takes one of Barney's items of fruit at random what is the probability it will be an apple? What is the probability it will not be an apple?

12 items of fruit. 4/12 are apples - can 4/12 be simplified? Yes both can be divided by 4 and so the fraction becomes = 1/3 for the probability of taking an apple.
The probability of NOT taking an ap...

Answered by James B. • Maths tutor

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