Question

It is given that: (question about integrals)

Answer 1

\[\int\limits_{1}^{3} f(x)dx=5\]

a) Write down \[\int\limits_{1}^{3} 2f(x)dx\]

b) Find the value of\[\int\limits_{1}^{3} (3x ^{2}+f(x))dx\]

Answer 2

\[\int\limits_{a}^{b} kf(x)dx\]\[=k\int\limits_{a}^{b} f(x)dx\]
By considering k=2, you can find the value for (a)

Answer 3

For (b)\[\int\limits_{1}^{3} (3x ^{2}+f(x))dx\]
\[=\int\limits_{1}^{3} (3x ^{2}) dx+\int\limits_{1}^{3}f(x)dx\]
can you try to do \[\int\limits_{1}^{3} (3x ^{2}) dx\]

Answer 4

oh ok, so in any expression with integrals, its the same as saying the integral of each term added/subtracted. For example, the next question is \[\int\limits_{2}^{4}(2f(x)-3g(x))\] would be:\[2\int\limits_{2}^{4}f(x)-3\int\limits_{2}^{4}g(x)\]
is that right?

Answer 5

you missed the 'dx', other than that it's right

Answer 6

ok thanks

Answer 7

Is the same true for derivatives? The next question asks \[d/dx (f(x)+g(x))\] would it be: \[d/dx(f(x))+d/dx(g(x))\]

Answer 8

yup