Question

Evaluate
∫
dx ) 1- x(
2
(a) x
5
/5 – 2/3 x
3
+ x + k
(b)
kx
3
x
3
+−
(c) 2x
(d) none of these
5.
∫
+
) x 1 ( ) 3x –1 (
dx is equal to
(a) x – x
2
– x
3
(b) x
3
– x
2
+ x (c) x – x
2
– x
3
+ k (d) none of these
6.
[
]
∫
x/1–x
dx is equal to
(a)
3
2
x
3/2
– 2 x
½
+k (b)
kx2x
3
2
+−
(c)
k
xx2
1
x2
1
++
(d) none of these
7. The integral of px
3
+ qx
2
+ rk + w/x is equal to
(a) px
2
+ qx + r + k
(b) px
3
/3 + qx
2
/2 + rx
(c) 3px + 2q – w/x
2
(d) none of these
8. Use method of substitution to integrate the function f(x) = ( 4x + 5 )
6
and the answer is
(a) 1/28 ( 4x + 5 )
7
+ k (b) ( 4x + 5 )
7
/7 + k (c) ( 4x + 5 )
7

9. Use method of substitution to evaluate
∫
+
52
)4x(x
dx and the answer is



10. Integrate ( x + a )
n
and the result will be

Answer 1

Answer on Question #54552-Math -Integral Calculus

4. Evaluate

$$\int (x ^ {2} - 1) d x = \frac {x ^ {3}}{3} - x + k.$$

Answer: (b) $\frac{x^3}{3} - x + k$ .

5.

$$\int (1 - 3 x) (1 + x) d x = \int (1 - 2 x - 3 x ^ {2}) d x = x - x ^ {2} - x ^ {3} + k.$$

Answer: (c) $x - x^{2} - x^{3} + k$ .

6.

$$\int \left(\sqrt {x} - \frac {1}{\sqrt {x}}\right) d x = \frac {2}{3} x ^ {\frac {3}{2}} - x ^ {\frac {1}{2}} + k.$$

Answer: (a) $\frac{2}{3} x^{\frac{3}{2}} - x^{\frac{1}{2}} + k$ .

7.

$$\int \left(p x ^ {3} + q x ^ {2} + r k + \frac {w}{x}\right) d x = \frac {p x ^ {4}}{4} + \frac {q x ^ {3}}{3} + r k x + w \ln x + C.$$

Answer: (d) none of these.

8.

$$\int (4 x + 5) ^ {6} d x = \frac {1}{4} \int (4 x + 5) ^ {6} d (4 x + 5) = \frac {1}{27} (4 x + 5) ^ {7} + k.$$

Answer: (a) $\frac{1}{27} (4x + 5)^7 + k$ .

9.

$$\int x (x ^ {2} + 4) ^ {5} d x = \frac {1}{2} \int (x ^ {2} + 4) ^ {5} d (x ^ {2} + 4) = \frac {1}{12} (x ^ {2} + 4) ^ {6} + k.$$

Answer: (b) $\frac{1}{12} \left(x^2 + 4\right)^6 + k$ .

10.

$$\int (x + a) ^ {n} d x = \frac {(x + a) ^ {n + 1}}{n + 1} + k.$$

Answer: (a) $\frac{(x + a)^{n + 1}}{n + 1} + k$ .

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