What is area y=e^{5x},y=e^{6x},x=1 ?

The answer to area y=e^{5x},y=e^{6x},x=1 is (5e^6-6e^5+1)/(30)

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area y=e^{5x},y=e^{6x},x=1

area

y = e^{5 x}, y = e^{6 x}, x = 1

\frac{5 e ^{6} - 6 e ^{5} + 1}{30}

Decimal Notation

37.58883 \dots

Solution steps

Apply the area formula:

\int_{0}^{1} e^{5 x} - e^{6 x} d x

Solve

\int_{0}^{1} e^{5 x} - e^{6 x} d x : \frac{5 e ^{6} - 6 e ^{5} + 1}{30}

The area is:

= \frac{5 e ^{6} - 6 e ^{5} + 1}{30}

\frac{d}{d x} (2 x y^{3})

x^{3} - 10 x^{2} + 16 x, - x^{3} + 10 x^{2} - 16 x

n = 0 \sum \infty \frac{1}{2 ^{n}}

\frac{d}{d x} ((x^{2} - 5 x + 3) (4 x^{3} + 10 x - 5))

f (x) = x^{2} - 11 y^{2}

What is area y=e^{5x},y=e^{6x},x=1 ?
The answer to area y=e^{5x},y=e^{6x},x=1 is (5e^6-6e^5+1)/(30)