What is the integral from sin(x) to cos(x) of e^t ?

The integral from sin(x) to cos(x) of e^t is e^{cos(x)}-e^{sin(x)}

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integral from sin(x) to cos(x) of e^t

\int_{s i n (x)}^{c o s (x)} e^{t} d t

e^{c o s (x)} - e^{s i n (x)}

Solution steps

\int_{s i n (x)}^{c o s (x)} e^{t} d t

Use the common integral:

\int e^{t} d t = e^{t}

= [e^{t}]_{s i n (x)}^{c o s (x)}

Compute the boundaries:

e^{c o s (x)} - e^{s i n (x)}

= e^{c o s (x)} - e^{s i n (x)}

\int_{0}^{5} \frac{1}{x - 1} d x

\int_{0}^{2 π} cos (2 t) d t

\int_{0}^{\frac{π}{6}} cos^{- 3} (2 x) sin (2 x) d x

\int_{1}^{e} \frac{ln ( x ^{2} )}{x} d x

\int_{0}^{2 π} 1 - cos (x) d x

What is the integral from sin(x) to cos(x) of e^t ?
The integral from sin(x) to cos(x) of e^t is e^{cos(x)}-e^{sin(x)}