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Integrate, with respect to x, xCos3x

Integration by parts: u = x u' = 1v' = Cos3x v = (Sin3x)/3 + c So, ∫xCos3x= (XSin3x)/3 - ∫(Sin3x)/3 dx= (XSin3x)/3 - 1/3( - (Cos3x)/3) + c = (XSin3x)/3 + (Cos3x)/9 + c
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I don't fully understand the purpose of integration. Could you please explain it to me?

I have written "..." where I imagine the student is replying. I have then provided prompts assuming that the student did not come up with the answer straight away. The scenario could be very differ...
RL
Answered by Rebecca L. • Maths tutor
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Integrate (sin(2x) + e^(2x+3))dx

1/2cos(2x) +1/2e^(2x+3) + C
HT
Answered by Hazel T. • Maths tutor
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For a graph C with equation y=3/(5-3x)^2, find the the equation of the line normal to the graph at point P, where x=2. Give your answer in the form ax+by+c=0

Find out the value of the y coordinate where x=2y=3/(5-3(2))^2=3Differentiate function in order to find the gradient of the graph at point Py=3/(5-3x)^-2Use chain rule where u=5-3xdu/dx=-3dy/dx=3u^-2Hence dy...
JI
Answered by Jazib I. • Maths tutor
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What are radians, why can't we just use degrees?

When you start your A Level, radians can seem very daunting because you've never seen them before and pi seems a very confusing number to use in relation to angles. But trust me, if you embrace radians they ...
MR
Answered by Matthew R. • Maths tutor
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