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Integrate the following expression with respect to x by parts: (2*x)*sin(x)

The integration by parts formula: S:u dv/dx = u v - S:v*du/dx, where S: means "Integral of with respect to x" Let 2*x be u and sin(x) be dv/dx So du/dx =2 and v= -cos(x) So S:(2 x) sin(x) = (2 x) (...
DP
Answered by David P. • Maths tutor
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When I integrate by parts how do I know which part of the equation is u and v'?

To determine which function is your u value in the by parts equation, you can use the acronym LATE to find the order of precedence for this value. LATE stands for: Logarithmic functions Arithmetric functions...
BA
Answered by Ben A. • Maths tutor
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A car is moving on an inclined road with friction acting upon it. When it is moving up the road at a speed v the engine is working at power 3P and when it is moving down the road at v the engine is working at a power P. Find the value of P.

Incline is at θ where sin θ = 1/20 and mass of the car is 800kg and v is 12.5 m/s Up the road: Power = Fv F = R + (800g)/20 Power = (R + 40g)*25/2 = 3P …. P = (R + 40g)*25/6 Down the road: Power = Fv F = R –...
JM
Answered by Jonathan M. • Maths tutor
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Integrate x*ln(x)

Let u = ln(x) and dv/dx = x Thus du/dx = 1/x and v = x 2 /2 Using the formula: Integral of u dv/dx = u v - Integral of v*du/dx This becomes: Integral of x*ln(x) = (x 2 ln(x))/2 - Integral of x/2 Completing t...
AG
Answered by Anindita G. • Maths tutor
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Differentiate the function f(x) = 2x^3 + (cos(x))^2 + e^x

When differentiating a function that is the sum of three different parts we can differentiate each part separately: a) 2x 3 is easy to differentiate. We remember the rule d/dx[ax b ] = abx b-1 . So 2x 3 --&g...
SP
Answered by Seth P. • Maths tutor
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