What is area y=e^x,y=e^{3x},x=ln(2),x=ln(3) ?

The answer to area y=e^x,y=e^{3x},x=ln(2),x=ln(3) is 16/3

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area y=e^x,y=e^{3x},x=ln(2),x=ln(3)

area

y = e^{x}, y = e^{3 x}, x = ln (2), x = ln (3)

\frac{16}{3}

Decimal

5.33333 \dots

Solution steps

Apply the area formula:

\int_{l n (2)}^{l n (3)} e^{x} - e^{3 x} d x

Solve

\int_{l n (2)}^{l n (3)} e^{x} - e^{3 x} d x : \frac{16}{3}

The area is:

= \frac{16}{3}

d er i v a t i v e [x + (x + sin^{2} (x))^{5}]^{7}

d er i v a t i v e 6 (2 x^{3} + 3) 6 x^{2}

\int \frac{2 - 4 x ^{2}}{x - x ^{3}} d x

t an g e n t y = F - x^{2} - x, at x = - 2

d er i v a t i v e f (x) = 10 t

What is area y=e^x,y=e^{3x},x=ln(2),x=ln(3) ?
The answer to area y=e^x,y=e^{3x},x=ln(2),x=ln(3) is 16/3