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Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Heres our integral: int(xsin(4x²)dx)The first decision to make is what to use as our substitution. We're going to go for the term tied up in the sine function: 4x²Set u = 4x²

Answered by Benjamin C. • Maths tutor

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A kettle has a 55% energy efficiency. The input energy for the kettle is 378,000 J per boil. Calculate the amount of energy dissipated in 5 boils.

Energy used for one boil = (3.78 x 10⁵/ 100) x 55Energy used for one boil = 2.079 x 10⁵J Energy lost per boil = 3.78 x 10⁵-2.079 x 10⁵Energy lost per boil = ...

Answered by Ryan A. • Physics tutor

3990 Views

Explain what is meant by the term placebo, and how a placebo would be utilised in a clinical trial of a novel pain relief medication

A placebo is a control method to account for perceived effects of taking a medication. This is because patients often report that they feel a difference from taking a medication, irrespective of whether i...

Answered by Ryan A. • Biology tutor

6865 Views

Find the 1st derivative of y = x^2 + 7x +3 and hence find the curves minima.

Firstly, we differentiate y = x²+7x+3 . This gives dy/dx = 2x+7.The minimum value occurs when dy/dx = 0. So find x and y when dy/dx=0. 2x+7=0 implies x= -3.5, which from the first equation mean...

Answered by Connor W. • Maths tutor

3799 Views

How do I respond to a Shakespeare extract?

Read the question carefully. Don't be afraid to underline keywords in the question. Often exam papers will ask you to write about themes like love, confusion, war and greed. If you see a ...

Answered by James C. • English tutor

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