- Evaluate \(\displaystyle \int_{0}^{\frac{\pi}{3}} \sin(x)\,dx\). (1 mark)
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- 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)
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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 5
The function with rule `f(x)` has derivative `f′(x) = cos\ 3x`.
If `f(pi/6) = 1,` find `f(x).` (3 marks)
Calculus, MET1 SM-Bank 25
Evaluate `int_0^(pi/4) cos 2x\ dx`. (2 marks)
Calculus, MET1 2007 HSC 2bi
Find an anti-derivative of `(1 + cos 3x)` with respect to `x`. (2 marks)
Calculus, MET1 2010 VCAA 2
Find an antiderivative of `cos (2x + 1)` with respect to `x.`
Calculus, MET1 2014 VCAA 7
If `f′(x) = 2cos(x) - sin(2x)` and `f(pi/2) = 1/2`, find `f(x)`. (3 marks)
Calculus, MET2 2012 VCAA 7 MC
The temperature, `T^@C`, inside a building `t` hours after midnight is given by the function
`f: [0, 24] -> R,\ T(t) = 22 - 10\ cos (pi/12 (t - 2))`
The average temperature inside the building between 2 am and 2 pm is
- `10°text(C)`
- `12°text(C)`
- `20°text(C)`
- `22°text(C)`
- `32°text(C)`