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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
)
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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| Evaluate following indefinite integrals
containing quadratic polynomial,
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| Example:
a
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Evaluate |
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| Solution: |
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| The indefinite integrals
containing quadratic polynomial of the form
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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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| solution: |
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Let's
Evaluate
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| by substituting
in the numerator |
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obtained
is
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