What is area y=e^{3x},y=e^{6x},x=1 ?

The answer to area y=e^{3x},y=e^{6x},x=1 is (e^6-2e^3+1)/6

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area y=e^{3x},y=e^{6x},x=1

area

y = e^{3 x}, y = e^{6 x}, x = 1

\frac{e ^{6} - 2 e ^{3} + 1}{6}

Decimal Notation

60.70961 \dots

Solution steps

Apply the area formula:

\int_{0}^{1} e^{3 x} - e^{6 x} d x

Solve

\int_{0}^{1} e^{3 x} - e^{6 x} d x : \frac{e ^{6} - 2 e ^{3} + 1}{6}

The area is:

= \frac{e ^{6} - 2 e ^{3} + 1}{6}

\int x^{3} (7 - x^{2})^{\frac{1}{2}} d x

y^{^{'}} = e^{9 x} - 4 x

\int e^{- 2 x^{2}} \cdot (- 4) x^{3} d x

n = 1 \sum \infty 8 (0.2)^{n}

n = 1 \sum \infty (1 + \frac{3}{n})^{n}

What is area y=e^{3x},y=e^{6x},x=1 ?
The answer to area y=e^{3x},y=e^{6x},x=1 is (e^6-2e^3+1)/6