- Evaluate \(\displaystyle \int_{0}^{\frac{\pi}{3}} \sin(x)\,dx\). (1 mark)
--- 3 WORK AREA LINES (style=lined) ---
- Hence, or otherwise, find all values of \(k\) such that \(\displaystyle \int_{0}^{\frac{\pi}{3}} \sin(x)\,dx=\displaystyle \int_{0}^{\frac{\pi}{2}} \cos(x)\,dx\), where \(-3\pi<k<2\pi\). (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
Calculus, MET2 2019 VCAA 4 MC
`int_0^(pi/6) (a sin (x) + b cos(x))\ dx` is equal to
- `((2 - sqrt 3)a - b)/2`
- `(b - (2 - sqrt 3) a)/2`
- `((2 - sqrt 3)a + b)/2`
- `((2 - sqrt 3) b - a)/2`
- `((2 - sqrt 3) b + a)/2`
Calculus, MET1 SM-Bank 4
Evaluate `int_0^(pi/2) sin (x/2)\ dx`. (3 marks)
Calculus, MET1 2013 VCAA 3
The function with rule `g(x)` has derivative `g prime (x) = sin (2 pi x).`
Given that `g(1) = 1/pi`, find `g(x).` (2 marks)
Calculus, MET1 2014 VCAA 7
If `f′(x) = 2cos(x) - sin(2x)` and `f(pi/2) = 1/2`, find `f(x)`. (3 marks)