1
WB JEE 2021
+2
-0.5
Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx}$$. Then
A
$${{\sqrt 3 } \over 8} \le I \le {{\sqrt 2 } \over 6}$$
B
$${{\sqrt 3 } \over {2\pi }} \le I \le {{2\sqrt 3 } \over \pi }$$
C
$${{\sqrt 3 } \over 9} \le I \le {{\sqrt 2 } \over {16}}$$
D
$$\pi \le I \le {{4\pi } \over 3}$$
2
WB JEE 2020
+1
-0.25
The value of

$$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^{10} {} \int\limits_{2n}^{2n + 1} {{{\sin }^{27}}} x\,dx$$ is equal to
A
27
B
54
C
$$-$$54
D
0
3
WB JEE 2020
+1
-0.25
$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to
A
1
B
$$5 - \sqrt 2 - \sqrt 3$$
C
$$3 - \sqrt 2$$
D
8/3
4
WB JEE 2020
+1
-0.25
Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over n}} f\left( {{j \over n}} \right)$$ is
A
$${1 \over 2}\int\limits_0^{{1 \over 2}} {f(x)\,} dx$$
B
$$\int\limits_{{1 \over 2}}^1 {f(x)\,} dx$$
C
$$\int\limits_0^1 {f(x)\,} dx$$
D
$$\int\limits_0^{{1 \over 2}} {f(x)\,} dx$$
EXAM MAP
Medical
NEET