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Why don't I have to put the +C after my answer for a definite integral?

When you evaluate a definite integral, we can think about using the "+C" and see what happens. Let's take (INT)2x dx between 2 and 3. We then have [x²+C] between 2 and 3. For x=3 we h...

Answered by Joseph C. • Maths tutor

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Integrate 1 / x(2sqrt(x)-1) on [1,9] using x = u^2 (u > 0).

Differentiate x = u²to get dx = 2u du. We need to change the limits, too:

1 <= x <= 9 <==> 1 <= u² <= 9 <==> 1 <= u <= 3 (since we are give...

Answered by Tutor69809 D. • Maths tutor

4964 Views

Show that, for all a, b and c, a^log_b (c) = c^log_b (a).

We want to prove:

a^log_b(c) = c^log_b(a).

Recall that we can always write x = e^ln(x), so x^y = (e^ln(x))^y

Answered by Tutor69809 D. • Maths tutor

6661 Views

Sketch the curve y = x^2 - 6x + 5, identifying roots and minima/maxima.

Remeber the formula: (a - b)² = a² - 2ab + b². Notice that y = x² - 23x + 5, so we want to write this using (x - 3)

Answered by Tutor69809 D. • Maths tutor

5296 Views

How would a reduction in interest rates lead to an increase in Economic Growth?

A reduction in interest rates would lead to a boost in Aggregate Demand and therefore an increase in real national output. If the monetary policy committee decide to reduce interest rates then the incenti...

Answered by Sebastian C. • Economics tutor

2184 Views