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MTH112: Calculus II-2025SPRG-LECT-02

MTH112: Calculus II-2025SPRG-LECT-02

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False

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Evaluate the following integral

$integral fraction numerator cos h x over denominator square root of sin h squared x minus 2 sin h x end root end fraction d x$

None

$sin h to the power of negative 1 end exponent open parentheses fraction numerator sin h x over denominator square root of 2 end fraction close parentheses plus C$

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Evaluate the following integral

$integral fraction numerator 1 over denominator square root of x squared plus 4 x plus 5 end root end fraction d x$

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None

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$sin h to the power of negative 1 end exponent open parentheses fraction numerator x plus 4 over denominator 2 end fraction close parentheses plus C$

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$sin h to the power of negative 1 end exponent open parentheses fraction numerator x plus 2 over denominator 2 end fraction close parentheses plus C$

❌

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$integral fraction numerator x over denominator 1 plus x squared end fraction d x equals space ln space open parentheses square root of 1 plus x squared end root close parentheses plus C$

True

False

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Evaluate the following integral

$integral fraction numerator 1 over denominator space square root of 4 x squared minus 1 end root space cos h to the power of negative 1 end exponent 2 x end fraction d x$

None

❌

$1 half space ln open parentheses fraction numerator 1 over denominator cos h 2 x end fraction close parentheses space plus C$

$integral fraction numerator x over denominator square root of 1 plus x squared end root end fraction d x equals 2 square root of 1 plus x squared end root plus C$

True

False

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Evaluate the following integral

$integral fraction numerator e to the power of negative x end exponent over denominator 1 plus e to the power of negative x end exponent end fraction d x$

None

❌

$ln open parentheses fraction numerator 1 over denominator 1 plus e to the power of negative x end exponent end fraction close parentheses space plus C$

✅

❌

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$integral fraction numerator e to the power of 2 x end exponent over denominator 4 plus e to the power of 2 x end exponent end fraction d x$ $equals integral fraction numerator 1 over denominator 8 plus 2 u end fraction space d u$

What substitution did we make?

None

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✅

❌

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Evaluate the following integral

$integral fraction numerator 1 over denominator square root of 1 plus tan h x end root open parentheses 1 plus sin h squared x close parentheses end fraction d x$

None

$integral fraction numerator cos x over denominator 1 plus cos squared x end fraction d x$ $equals integral fraction numerator 1 over denominator 2 minus u squared end fraction space d u$