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| Integral
calculus |
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The
indefinite integral |
The indefinite integrals
containing quadratic polynomial (trinomial)
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The indefinite integrals
containing quadratic polynomial, examples
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The indefinite integrals
containing quadratic polynomial (trinomial)
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| Recall
that the quadratic polynomial y
= ax2 + bx + c
represents the expansion of the translatable form of
its source function y
= ax2 in the direction of the coordinate axes, thus
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| a
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Solution:
if b2
-
4ac < 0
substitutions,
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| b
)
Solution: if b2
-
4ac > 0
substitutions,
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| c
) Solution: if b2
-
4ac = 0
then k
= 0, substitution
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gives |
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The indefinite integrals
containing quadratic polynomial, examples
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| Example:
53.
a
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Evaluate |
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| Example:
53.
b
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Evaluate |
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| Example:
53.
c
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Evaluate |
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Since the numerator of the integrand
is the derivative of the denominator therefore, the substitution
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t = ax2
+ bx + c
and dt =
(2ax + b) dx
gives
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| by substituting
in the numerator |
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| Example:
54.
a
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Evaluate |
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| Calculus contents
F |
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