The Indefinite Integral (HSC SSCE Mathematics Advanced): Quizzes

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The Indefinite Integral
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What does an indefinite integral represent?

General primitive of a function

Why must we include the constant CC when finding indefinite integrals?

Infinitely many primitives differ by CC

What is the key difference between definite and indefinite integrals?

Definite gives number; indefinite gives fn

Find ∫12x3 dx\int 12x^3 \, dx

3x4+C3x^4 + C

Find ∫(3x+1)5 dx\int (3x + 1)^5 \, dx

118(3x+1)6+C\frac{1}{18}(3x + 1)^6 + C

Why can't we use standard forms when n=−1n = -1?

It creates division by zero

Find ∫12x3 dx\int \frac{12}{x^3} \, dx

−6x2+C-\frac{6}{x^2} + C

Find ∫(x3−1)2 dx\int (x^3 - 1)^2 \, dx by expanding first

x77−x42+x+C\frac{x^7}{7} - \frac{x^4}{2} + x + C

Express x\sqrt{x} in fractional index form for integration

x12x^{\frac{1}{2}}

Find ∫dx9−2x\int \frac{dx}{\sqrt{9 - 2x}}

−9−2x+C-\sqrt{9 - 2x} + C

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