Question

Integrate the function

$\huge\green\tt\frac{ \sqrt{tanx} }{sinxcosx}$

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Answer 1

Step-by-step explanation:

$\sf\large\underline{Given:-}$

$\sf{\implies Principal=Rs.2000}$

$\sf{\implies Time\:_{(compound\: annually)}=3\dfrac{1}{4}\:years}$

$\sf{\implies Rate\:_{(compound\: interest)}=10\%}$

$\sf\large\underline{To\:Find:-}$

$\sf{\implies Amount\:_{(at\:the\:end\:of\:the\: year)}=?}$

$\sf\large\underline{Solution:-}$

To calculate the amount on the sum of 2000 for 3 whole 1/4 years at the rate of 10% compounded annually. Just applying a formula. But note here in the given Question the time is given in fractional form so we have to apply a fractional formula to calculate the amount:]

$\sf\large\underline{Formula\:used:-}$

$\tt{\implies A=P\bigg(1+\dfrac{r}{100}\bigg)^n\bigg(1+\dfrac{rF}{100}\bigg)}$

Here, n=3 year , F=1/4

$\tt{\implies A=2000\bigg(1+\dfrac{10}{100}\bigg)^3\bigg(1+\dfrac{10*1}{100*4}\bigg)}$

$\tt{\implies A=2000\bigg(1+\dfrac{1}{10}\bigg)^3\bigg(1+\dfrac{1}{40}\bigg)}$

$\tt{\implies A=2000\bigg(\dfrac{10+1}{10}\bigg)^3\bigg(\dfrac{40+1}{40}\bigg)}$

$\tt{\implies A=2000\bigg(\dfrac{11}{10}\bigg)^3\bigg(\dfrac{41}{40}\bigg)}$

$\tt{\implies A=2000*(1.1)^3*\dfrac{41}{40}}$

$\tt{\implies A=2000*1.331*\dfrac{41}{40}}$

$\tt{\implies A=2662*\dfrac{41}{40}}$

$\tt{\implies A=66.55*41}$

$\tt{\implies A=Rs.2728.55}$

$\sf\large{Hence,}$

$\sf{\implies Amount\:_{(received\:by\:Heena)}=Rs.2728.55}$

Answer 2

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