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Use Integration by parts to find ∫ xsin3x dx

∫ xsin3x dx takes the form of any integral ∫ (u)(dv/dx) dx. ∫ (u)(dv/dx) dx = uv - ∫ (v)(du/dx) dx Taking u=x and dv/dx= sin3x. The equation can be re-written in the form uv - ∫ (v)(du/dx) dx. Therefore, ∫ x...
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Answered by Safiyyah V. • Maths tutor
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The graph of y = x^2 + 4x - 3 (Graph A) is translated by the vector (3 | 2), find the equation of the new graph (Graph B)

Minimum point of Graph A:*complete square to find(x+2)^2 - 4 - 3 = 0(x+2)^2 - 7 = 0Therefore minimum point = (-2, -7)Minimum point of Graph B:(-2+3, -7+2) = (1, -5)*reverse complete the square method(x-1)^2 ...
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Answered by George B. • Maths tutor
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Why does ionisation energy decrease down group 2?

As you descend group 2, more electrons are present in the atom. These electrons fill subshells at a greater energy level. There is a greater distance between the outer shell electron and the nucleus, as well...
Answered by • Chemistry tutor
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In our macro-economic models, we always input a central bank interest rate. Yet, when I go to the bank to borrow money, I get a much higher interest rate. How does a higher or lower interest rate effect lending if I can't borrow at that rate anyway?

While this is not necessarily relevant for the IB exams, it is important to keep in mind that the interest rate that we use in the macro-economic models like the AD/AS model is an approximation of cost of le...
Answered by • Economics tutor
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Find the volume of a cone with radius 13cm and with a perpendicular height of 9cm.

volume= 1/3( πr 2 )h= 1/3 (3.14x 13x 13)x9= 1592.79 cm 3 (2.d.p) = 1590 cm 3 (3.s.f) r= radius h= perpendicular height
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Answered by Meghan B. • Maths tutor
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