Question

Integration limit 0 to π/2 sinx dx

Answer 1

Answer:

$\boxed{\mathfrak{ \int \limits_0^{ \dfrac{\pi}{2}} sinx. dx = 1}}$

Explanation:

$\rm Compute \: the \: definite \: integral: \\ \rm \implies \int \limits_0^{ \dfrac{\pi}{2}} sinx. dx \\ \\ \rm Apply \: the \: fundamental \: theorem \: of \: calculus. \\ \rm The \: antiderivative \: of \: sinx \: is \: -cosx: \\ \rm \implies - cosx \Big|_0^ {\dfrac{\pi}{2} } \\ \\ \rm Evaluate \: the \: antiderivative \: at \: the \: limits \: and \\ \rm subtract. \\ \rm \implies - cos \dfrac{\pi}{2} - ( - cos0) \\ \\ \rm \implies - cos 90 \degree - ( - 1) \\ \\ \rm \implies - 0 + 1 \\ \\ \rm \implies 1$