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MTH112: Calculus II-2025SPRG-LECT-02

MTH112: Calculus II-2025SPRG-LECT-02

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Evaluate the following integral e^x cos4x dx

( e ͯ /17 ) ( 4 sin4x + cos4x) +C

✅

( e ͯ /17 ) ( 4 sin4x - cos4x) +C

❌

( e ͯ /4 ) ( 4 sin4x + cos4x) +C

❌

( e ͯ /16 ) ( 4sin4x + cos4x) +C

❌

None

❌

( e ͯ /17 ) ( sin4x + 4 cos4x) +C

❌

( e ͯ /17 ) ( sin4x + cos4x) +C

❌

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Evaluate the following integral

None

Evaluate the following integral

$x to the power of 4 over 4 space fraction numerator e to the power of x squared end exponent over denominator 2 x end fraction plus C$

None

$x cubed space fraction numerator e to the power of x squared end exponent over denominator 2 x end fraction plus x to the power of 4 over 4 e to the power of x squared end exponent plus C$

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How many times do you have to apply Integration by parts technique to evaluate the integration

x¹ dx

None

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How many times do you have to apply Integration by parts technique to evaluate the integration

x⁷ cos( x²) dx

❌

None

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x⁹ ln(10 x) dx = ( x¹⁰/ 100 ) (.............................) + C

Evaluate the following integral

❌

$fraction numerator x 3 space over denominator 3 end fraction sin x plus C$

None

Evaluate the following integral

$open parentheses x cubed over 3 space open parentheses ln x close parentheses squared plus fraction numerator 2 x cubed over denominator 9 end fraction space ln x space minus fraction numerator 2 x cubed over denominator 27 end fraction close parentheses plus C$