1 Marks Question

Question 11 Mark

Evaluate the following integrals:
$\int\text{x}^4\text{dx}$

Answer

$\int\text{x}^4\text{dx}=\frac{\text{x}^{4+1}}{4+1}+\text{c}$
$=\frac{\text{x}^5}{5}+\text{c}$

Question 21 Mark

Evaluate $\int\frac{1-\sin\text{x}}{\cos^2\text{x}}\text{ dx}$

Answer

Let $\text{I}=\int\frac{1-\sin\text{x}}{\cos^2\text{x}}\text{ dx}$
$=\int\sec^2\text{x dx}-\int\sec\text{x}\tan\text{x dx}$
$\text{I}=\tan\text{x}-\sec\text{x}+\text{C}$

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Question 31 Mark

Evaluate the following integrals:
$\int\log_\text{x}\text{xdx}$

Answer

$\int\log_\text{x}\text{xdx}$
$=\int1.\text{dx}$
$=\text{x}+\text{c}$

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Question 41 Mark

Evaluate $\int\sec^2(7-4\text{x})\text{dx}$

Answer

$\int\sec^2(7-4\text{x})\text{dx}$
$=\frac{\tan(7-4\text{x})}{-4}+\text{C}$ $(\because\sec^2\text{x}=\tan\text{x}+\text{C})$

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Question 51 Mark

Evaluate the following integrals:
$\int3^\text{x}\text{dx}$

Answer

$\int3^\text{x}\text{dx}=\frac{3^\text{x}}{\log3}+\text{c}\ \ \Big[\because\ \int\text{a}^\text{x}\text{dx}=\frac{\text{a}^\text{x}}{\log\text{a}}+\text{c}\Big]$

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Question 61 Mark

Evaluate $\int2^{\text{x}}\text{ dx}$

Answer

Let $\text{I}=\int2^{\text{x}}\text{ dx}$
$\text{I}=\frac{2^{\text{x}}}{\log_\text{e}2}+\text{C}$

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