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Integrate 2sin^3(x)+3.

First we need to use trigonometric identities to convert the sin^3(x) to a single power. This is because we cannot integrate trigonometric functions that are above the power of 1. We need to use the double a...
VP
Answered by Vaidik P. • Maths tutor
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A curve with equation y=f(x) passes through the point (1, 4/3). Given that f'(x) = x^3 + 2*x^0.5 + 8, find f(x).

We know that f'(x) = x^3 + 2*x^0.5 + 8, and we can integrate both sides. This gives us f(x) = (1/4)*x^4 + (4/3) x^(3/2) + 8 x + c, remembering to add the constant of integration. Now, we are almost there, bu...
GC
Answered by George C. • Maths tutor
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Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.

= (4/3)x 3 - (10/2)x 2 + x 1/2 /(1/2) + C = (4/3)x 3 - 5x 2 + 2x 1/2 + C
AA
Answered by Aisha A. • Maths tutor
4110 Views

Can you explain the sum of 1 to 100?

The idea here is to pair your numbers up to get to the solution. If you were to put this through a calculator it would take you a while. However, if we simplify the problem to the sum of 1 to 10 you'll be ab...
JS
Answered by Jasivan S. • Maths tutor
4108 Views

Find the exact solution, in its simplest form, to the equation ln(4y + 7) = 3 + ln(2 – y) (Core Maths 3 Style Question)

First we subtract ln(2-y) from both sides to get "ln(4y+7) - ln(2-y) = 3". By applying the laws of logs from C2, we have "ln[(4y+7)/(2-y)] = 3". Therefore, if we put them as exponents of ...
DB
Answered by Danielle B. • Maths tutor
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