Exponential integration Quiz 1

Question 1

Integrate $$y-7x={{e}^{2x}}$$ with respect to $$'x'$$.

Accepted Answer

$$\dfrac{{{e}^{2x}}}{2}+\dfrac{7}{2}{{x}^{2}}+c$$

Answer

$$\dfrac{{{e}^{2x}}}{2}+\dfrac{7}{2}x+c$$

Answer

$$\dfrac{{{e}^{2x}}}{2}+7{{x}^{2}}+c$$

Answer

$$\dfrac{{{e}^{2x}}}{2}+7x+c$$

Question 2

Find the antiderivative of $${{e}^{x}}\sqrt{7+4{{e}^{x}}}$$.

Accepted Answer

$$\dfrac{1}{6}{{\left( 7+4{{e}^{x}} \right)}^{\frac{3}{2}}}+c$$

Answer

$$\dfrac{1}{6}{{\left( 7+4{{e}^{2x}} \right)}^{\frac{3}{2}}}+c$$

Answer

$$\dfrac{1}{6}{{\left( 7+4{{e}^{x}} \right)}^{\frac{2}{3}}}+c$$

Answer

$$\dfrac{1}{6}{{\left( 7+4{{e}^{{{x}^{2}}}} \right)}^{\frac{3}{2}}}+c$$

Question 3

Find the antiderivative of $$'uv'$$with respect to $$'x'$$where $$u=3{{x}^{2}}	ext{ and }v={{e}^{2x}}^{^{3}}$$.

Accepted Answer

$$\dfrac{1}{2}{{e}^{2{{x}^{3}}}}+c$$

Answer

$$\dfrac{1}{2}{{e}^{2{{x}^{2}}}}+c$$

Answer

$$\dfrac{1}{2}{{e}^{3{{x}^{2}}}}+c$$

Answer

$$\dfrac{2}{3}{{e}^{2{{x}^{3}}}}+c$$

Question 4

Evaluate: $$\int\limits_{1}^{2}{{{e}^{1-x}}dx}$$

Accepted Answer

$$-{{e}^{-1}}+1$$

Answer

$$-{{e}^{-1}}-1$$

Answer

$$-{{e}^{1}}+1$$

Answer

$$-\dfrac{1}{{{e}^{-1}}}+1$$

Question 5

Integrate $$q'(x)=-0.015{{e}^{-0.01x}}$$ and find the approx. value of the integration constant if $$q(50)=2.35	ext{ and }{{e}^{-0.5}}=	ext{0}.60666$$

Accepted Answer

$$1.44$$

Answer

$$14.4$$

Answer

$$1.404$$

Answer

$$1.24$$