Integration by substitution Quiz 1

Question 1

Write the value of integration $$I$$ where, $$I=\int{\left( 340m+182 \right).{{e}^{85{{m}^{2}}+91m-110}}dm}$$

Accepted Answer

$$2{{e}^{85{{m}^{2}}+91m-110}}+c$$

Answer

$$2{{e}^{91m-110}}+c$$

Answer

$${{e}^{85{{m}^{2}}+91m-110}}+c$$

Answer

$$2{{e}^{85{{m}^{2}}+91m}}+c$$

Question 2

Simplify the integral $$\int{\dfrac{\sin \left( {{	an }^{-1}}19k ight)}{1+361{{k}^{2}}}}dk$$

Accepted Answer

$$-\dfrac{1}{19}\cos \left( {{	an }^{-1}}19k ight)+c$$

Answer

$$-\dfrac{1}{19}	an \left( {{\cos }^{-1}}19k ight)+c$$

Answer

$$\dfrac{1}{19}	an \left( {{\cos }^{-1}}19k ight)+c$$

Answer

$$\dfrac{1}{19}\cos \left( {{	an }^{-1}}19k ight)+c$$

Question 3

Evaluate $$\int{{{\left( 289 \right)}^{15{{m}^{3}}+3m+93}}\left( 45{{m}^{2}}+3 \right)dm}$$

Accepted Answer

$${{\dfrac{\left( 289 \right)}{\log 289}}^{15{{m}^{3}}+3m+93}}+c$$

Answer

$${{\left( 289 \right)}^{15{{m}^{3}}+3m+93}}+c$$

Answer

$${{\dfrac{\left( 289 \right)}{\log 15}}^{15{{m}^{3}}+3m+93}}+c$$

Answer

$${{\dfrac{\left( 289 \right)}{\log 15}}^{15{{m}^{3}}+3m-93}}+c$$

Question 4

Write the value of integral $$\int{\left( {{2}^{x}}.\cos {{2}^{x}} \right)}.{{e}^{\sin {{2}^{x}}}}dx$$

Accepted Answer

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

Answer

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

Answer

$$\dfrac{1}{\log 2}.{{e}^{\operatorname{sinx}}}dx$$

Answer

$$\dfrac{1}{\log 2}.{{e}^{\cos x}}dx$$

Question 5

Simplify $$\int{{{e}^{\log 	an \left( {{h}^{2}}+5h-9 ight)}}.{{\sec }^{2}}\left( {{h}^{2}}+5h-9 ight)\left( 4h+10 ight)}dh$$

Accepted Answer

$${{	an }^{2}}\left( {{h}^{2}}+5h-9 ight)+c$$

Answer

$${{\sec }^{2}}\left( {{h}^{2}}+5h-9 \right)+c$$

Answer

$$\dfrac{1}{2}co{{\operatorname{t}}^{2}}\left( {{h}^{2}}+5h-9 \right)+c$$

Answer

$$\dfrac{1}{2}{{\sin }^{2}}\left( {{h}^{2}}+5h-9 \right)+c$$