Mathematics

# $\int_{ - 1}^2 {\sqrt {5x + 6} } dx$

##### SOLUTION
Let $5x+6=t$, then on differentiating the equation we get, $5dx=dt$.
When $x=-1$ then $t=5\times -1+6=1$ and $x=2$ then $t=5\times2+6=16$
Thus,
$\int _{ -1 }^{ 5 }{ \sqrt { 5x+6 } dx } \\=\dfrac { 1 }{ 5 } \int _{ 1 }^{ 16 }{ \sqrt { t } dt } \\=\dfrac { 1 }{ 5 } { \left[ \dfrac { { t }^{ \dfrac { 3 }{ 2 } } }{ \dfrac { 3 }{ 2 } } \right] }_{ 1 }^{ 16 }\\=\dfrac { 2 }{ 15 } \left[ { 16 }^{ \dfrac { 3 }{ 2 } }-1 \right] \\=\dfrac { 2 }{ 15 } \times 63\\=\dfrac { 42 }{ 5 }\\ =8\dfrac { 2 }{ 5 }$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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