જો $[t]$ એ મહત્તમ પૂર્ણાંક $\leq t$ દર્શાવે,તો $\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|+1\right] d x$ નું મૂલ્ય શોધો.
- A$\frac{\sqrt{37}+\sqrt{13}-4}{6}$
- B$\frac{\sqrt{37}-\sqrt{13}-4}{6}$
- C$\frac{-\sqrt{37}-\sqrt{13}+4}{6}$
- D$\frac{-\sqrt{37}+\sqrt{13}+4}{6}$
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ધારો કે $f(x) = 2 + |x| - |x - 1| + |x + 1|$,$x \in R$. ધ્યાનમાં લો:
$(S1): f^{\prime}\left(-\frac{3}{2}\right) + f^{\prime}\left(-\frac{1}{2}\right) + f^{\prime}\left(\frac{1}{2}\right) + f^{\prime}\left(\frac{3}{2}\right) = 4$
$(S2): \int_{-2}^{2} f(x) dx = 12$
તો,
$(S1): f^{\prime}\left(-\frac{3}{2}\right) + f^{\prime}\left(-\frac{1}{2}\right) + f^{\prime}\left(\frac{1}{2}\right) + f^{\prime}\left(\frac{3}{2}\right) = 4$
$(S2): \int_{-2}^{2} f(x) dx = 12$
તો,
DifficultJEE MAIN 2022
View Solution$\int_0^1 \sqrt{\frac{1-x}{1+x}} \,dx$ ની કિંમત શોધો.
MediumIIT 2004
View Solution$\int_{0}^{\infty} \frac{x}{(1+x)(x^{2}+1)} dx$ નું મૂલ્ય શું છે?
$\int_0^1 |5x - 3| \, dx = $
ટ્રેપેઝોઇડલ (Trapezoidal) નિયમનો ઉપયોગ કરીને, નીચે આપેલા ડેટાના આધારે $\int_1^4 y \, dx$ ની આશરે કિંમત શોધો:
$x$ $1$ $2$ $3$ $4$ $y$ $0.7111$ $0.7222$ $0.7333$ $0.7444$
($.1833$ માં)
| $x$ | $1$ | $2$ | $3$ | $4$ |
|---|---|---|---|---|
| $y$ | $0.7111$ | $0.7222$ | $0.7333$ | $0.7444$ |
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